Given the point (1, 2) and a slope of 4, write the equation in point slope form.
This article is about the math term. For other uses, see Slope (disambiguation).
For the grade (incline or gradient or pitch or slope) of any physical feature, see Grade (slope).
Slope: {\displaystyle m=\left({\frac {\Delta y}{\Delta x}}\right)=\tan(\theta )}{\displaystyle m=\left({\frac {\Delta y}{\Delta x}}\right)=\tan(\theta )}
In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.[1] Slope is often denoted by the letter m; there is no clear answer to the question why the letter m is used for slope, but its earliest use in English appears in O'Brien (1844)[2] who wrote the equation of a straight line as "y = mx + b" and it can also be found in Todhunter (1888)[3] who wrote it as "y = mx + c".[4]
Slope is calculated by finding the ratio of the "vertical change" to the "horizontal change" between (any) two distinct points on a line. Sometimes the ratio is expressed as a quotient ("rise over run"), giving the same number for every two distinct points on the same line. A line that is decreasing has a negative "rise". The line may be practical - as set by a road surveyor, or in a diagram that models a road or a roof either as a description or as a plan.
The steepness, incline, or grade of a line is measured by the absolute value of the slope. A slope with a greater absolute value indicates a steeper line. The direction of a line is either increasing, decreasing, horizontal or vertical.
A line is increasing if it goes up from left to right. The slope is positive, i.e. {\displaystyle m>0}m>0.
A line is decreasing if it goes down from left to right. The slope is negative, i.e. {\displaystyle m<0}m<0.
If a line is horizontal the slope is zero. This is a constant function.
If a line is vertical the slope is undefined (see below).
The rise of a road between two points is the difference between the altitude of the road at those two points, say y1 and y2, or in other words, the rise is (y2 − y1) = Δy. For relatively short distances, where the earth's curvature may be neglected, the run is the difference in distance from a fixed point measured along a level, horizontal line, or in other words, the run is (x2 − x1) = Δx. Here the slope of the road between the two points is simply described as the ratio of the altitude change to the horizontal distance between any two points on the line.
In mathematical language, the slope m of the line is
{\displaystyle m={\frac {y_{2}-y_{1}}{x_{2}-x_{1}}}.}m=\frac{y_2-y_1}{x_2-x_1}.
The concept of slope applies directly to grades or gradients in geography and civil engineering. Through trigonometry, the slope m of a line is related to its angle of incline θ by the tangent function
{\displaystyle m=\tan(\theta )}m = \tan (\theta)
Thus, a 45° rising line has a slope of +1 and a 45° falling line has a slope of −1.
what is 3,910 divided by 25 using the power of 10
A: 25
B: 250
C: 25,000
Answer:
izuocha is superior
Step-by-step explanation:
Answer:
ochaochaochaocha
Step-by-step explanation:
sorry i trying to get attention from someone
Simplify 3(2y -1) + 2y
Answer: 8y -3
Step-by-step explanation:
3(2y -1) + 2y
6y -3 + 2y
8y -3
Answer:
8 y - 3
Step-by-step explanation - I got it from google so its right 100%
I am solely here to brag!
I am officially a college student and only 14!
Next semester I will on top of my high school classes be taking college courses.
And by 11th grade be officially done with high school!
Answer:
That's wonderful!
Step-by-step explanation:
I'm really proud of you! I'm 14 (almost 15), and taking sophomore classes right now, and a foreign language. I absolutely regret not taking a second math class this year (Algebra II).
Marlene expects her gross income to be $54,000 this year, and she expects her required deductions to amount to $15,000. Her employer covers 90% of the cost of a $4800-per-year health insurance plan and 80% of the cost of a $900-per-year life insurance plan, with the remainder of the cost coming out of Marlene's pay, and Marlene also expects to contribute 8% of her gross income this year to her 401(k) plan. She wants to calculate how much she will receive for each of her bimonthly paychecks.
Answer:
Marlene will receive $1,417.50 for each of her bimonthly paychecks.
Step-by-step explanation:
This can be calculated using the following 3 steps:
Step 1: Calculation of annual deductions to bear by Marlene
Required deductions = $15,000
Contribution to cost of health insurance plan per-year = $4800 * 10% = $480
Contribution to cost of life insurance plan per-year = $900 * 20% = $180
Contribution to this year's 401(k) plan = $54,000 * 8% = $4,320
Step 2: Calculation of annual paychecks
Annual paychecks = Gross income - Required deductions - Contribution to cost of health insurance plan per-year - Contribution to cost of life insurance plan per-year - Contribution to this year's 401(k) plan = $54,000 - $15,000 - $480 - $180 - $4,320 = $34,020
Step 3: Calculation of bimonthly paychecks
Bimonthly paychecks = Annual paychecks / 24 = $34,020 / 24 = $1,417.50
Therefore, Marlene will receive $1,417.50 for each of her bimonthly paychecks.
Divide 4 1/4 by 2.
At the start of the month, Stephen’s savings account had a balance of $1,624. He made a $420 withdrawal each week for four weeks. During that month, he also made two deposits of $600 each and one deposit of $1,000. What was the balance in Stephen’s account at the end of the month?
Answer:
- 1625
Step-by-step explanation:
420 times 4 = 1680
1624 - 1680 = -56
-56 - 600 - 1000 = -1625
BRAINLIEST PLEASE
Olivia filled 6 baskets of strawberries. Later she combined the fruit evenly into 3 larger boxes. if all 3 boxes sold for $42, how much money did each box of strawberries cost?
Answer:
21
Step-by-step explanation:
becuase that's the answer lol
find the solution to the following system using substitution or elimination:
y = 3x + 2
y = -2x - 8
A. (-2, -4).
B. (-3/5, -34/5).
C. (-6/5, -8/5).
D. (1, 6)
Answer: A
Explanation:
Just use substitution because it's more efficient. Plug -2x-8 into y to make -2x-8=3x+2. Add 8 to both sides to get -2x=3x+10. Subtract 3x to both sides to get -5x=10. Divide -5 to both sides to get x=-2. Now, plug in x=-2 to one of the equations, let's use y=3x+2. The equation would be y=3(-2)+2. Multiply 3 and -2 to get -6. Add -6 to 2 and you'll result with y=-4.
What is the rate
$150/25
written as a unit rate?
A.
$30/5
B.
$6/1
C.
$4/1
D.
$125/2
Answer:
B
Step-by-step explan
150 divide by 25
25 divide by 25
Can anyone by chance know how to do these geometry questions?
Answer:
G is equal to (8, -11)
Step-by-step explanation:
We are given the midpoint and one end of the line segment. We can find the other end of it by taking the distance from H to M, doubling it, and adding that to H:
[tex]G(x, y) = H(x, y) + 2(M(x, y) - H(x, y))\\\\G_x = H_x + 2(M_x - H_x)\\G_x = -4 + 2(-6 - (-4))\\G_x = -4 + 2(-2)\\G_x = -4 - 4\\G_x = 8\\\\G_y = H_y + 2(M_y - H_y)\\G_y= 3 + 2(- 3 - 4)\\G_y= 3 - 6 - 8\\G_y = -11[/tex]
So the coordinates of endpoint G are (8, -11)
what is the answer to X - 8 < -2
Answer:
X>6
Step-by-step explanation:
X-8<-2
X<-2+8
X>6
because the sign changed from negative to positive, the inequality has to be flipped
Olivia can type 45 words every 2.5
minutes. What is the unit rate of words
per minute that Olivia can type?
What would be the rate of words per second?
Answer:
18 per min and 0.3 per second
Step-by-step explanation:
Per minut --> 45/2.5 = 18 words per minut
Per sec --> 2.5 mins*60 secs = 150 sec, then 45/150 = 0.3 words per second
Best regards
Help me pls ASAP thank you
Answer:
3rd option
Step-by-step explanation:
The input(x) does not repeat
I WILL GIVE BRAILYEST!!!!!
What are the solutions to y=5x2−35x+30?
What are the solutions to y=2x2+16x+30?
What are the solutions to y=6x2−48x+42?
Answer:
0,6
9,8
0,9
Step-by-step explanation:
5x - (2x + 5)
170
please help.
Answer:
56.66666667??? i think
Step-by-step explanation:
Answer:
The simplified answer is -335x-850
what is the simplified fractional equivalent of the terminating decimal 0.32
Answer:
8/25
Step-by-step explanation:
Brainliest pls
Answer:
8/25
Step-by-step explanation:
Write the word sentence as an equation. Then solve.
The quotient of a number x and −1.5 is 21.
Equation:
Question 2
Solution: x=
Answer:
-1.5-21x
Step-by-step explanation:
A robot can complete 3 tasks in hour. Each task takes the same amount of time. 10 a. How long does it take the robot to complete one task? b. How many tasks can the robot complete in one hour?
Answer:
a.20 minutes
b.3 tasks
Step-by-step explanation:
60 divided by 3 = 20
The club sold shirts and capes to raise money for new stage equipment. The club sold each shirt for $20.00. The club made profit of $4.00 for each shirt. Sold. Part A: The drama club sold a total of $480.00 worth of shirts. How much profit did the club make from the shirt sale?
Answer:
The club made a profit of $96 from the shirt sale.
Step-by-step explanation:
First, you have to find the number of shirts sold by dividing the total amount sold by the price per shirt:
480/20=24
Now, that you know the number of shirts that were sold, you can multiply the profit per shirt for the number of shirts sold:
4*24=96
According to this, the answer is that the club made a profit of $96 from the shirt sale.
Ifa line segment has a length of 12 units and after a dilation the image
length is 4 units, what was the scale factor?
A. 1/3
B. 3
C. 8
================================================
Work Shown:
x = preimage length = 12
y = image length = 4
z = scale factor
z = y/x
z = 4/12
z = (1*4)/(3*4)
z = 1/3
The scale factor is 1/3.
This means the image is 1/3 of the length of the preimage.
answer quickly !!! Pls
Answer:
(6 × 5) + (6 × 3) = 6 × (5 + 3)
Step-by-step explanation:
Since both 5 and 3 are being multiplied by 6, the total would be 6 multiplied by the sum of 5 and 3.
The equation 2x-7=5+x has exactly one solution. True or false
Answer:
True
Step-by-step explanation:
x=5+7=12
The only solution is x=12.
Elena wants to make a scale drawing of her bedroom. Her bedroom is a rectangle with length 5 m and width 3 m. She decides on a scale of 1 to 50. a. What would be the width and length of a scale drawing of Elena's bedroom?
Answer: Length = 10cm
Width = 6cm
Step-by-step explanation:
First and foremost, we should note that
1 meter = 100 cm.
Therefore,
Length = 5m = 500 cm
Breadth = 3m = 300 cm.
Since Elena wants to make a scale drawing of 1 to 50, then
Length = 500 cm / 50 = 10 cm
Breadth = 300 cm / 50 = 6 cm.
Therefore, the length of the scale drawing will be 10 cm and the width of the scale drawing will be 6cm.
i genuinely don't understand . please help me asap
Answer:
48.17
Step-by-step explanation:
Umm.. i don't really have time to explain but
A^2+B^2=C^2
36^2+32^2=48.17
Sorry I didn't know what subject to put this in but Please help I really do need it u don't have to tho
Which fitness test measures the strength and flexibility of the lower back?
A.
Walk/Run test
B.
Curl ups
C.
Sit and Reach
D.
Trunk Lift
Answer:
Curl ups
Step-by-step explanation:
I'm not 100% sure, but it seems like the most logical answer to me.
Answer:
Trunk Lift
Step-by-step explanation:
#12, what is this answer ?
Answer:
joan chris martin sara
Step-by-step explanation:
Brainliest for the correct answer 20 points!!!
Answer:
y = -3/2x + 3
Step-by-step explanation:
Answer:
y= 3 - 2x
Step-by-step explanation:
PLEASE HELP ME WITH THIS ASAP
9514 1404 393
Explanation:
1. ΔABC ≅ ΔDEF . . . . . 1. SAS postulate*
_____
The two given congruent sides are either side of the given congruent angle, so the SAS postulate applies. The objective appears to be irrelevant.
Billy Bob is filling his bathtub with water. At one minute, there are 5
gallons, at two minutes there are 8 gallons, and at 3 minutes there are
11 gallons of water in the tub.
If this pattern continues, how many gallons of water will be in the tub
at 7 minutes?
Answer:
There will be 23 gallons
Answer:
23 gallons
Step-by-step explanation:
the bathtub is filling by 3 more gallons every minute, 7-4=3, 4*3=12, 11+12=23
