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Answer:

Step-by-step explanation:

Slope of line passing through [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

From the graph attached,

Slope of the line passing through (-3, 0) and (0, 5) = [tex]\frac{5-0}{-3-0}[/tex]

                                                                                    = [tex]-\frac{5}{3}[/tex]

Line passing through a point (h, k) and slope 'm' will be,

y - h = m(x - k)

Since, line passing through (11, 0) is parallel to the line given in the graph,

Slope of the parallel line will be same as [tex]-\frac{5}{3}[/tex]

Equation of a line passing through (11, 0) and slope = [tex]-\frac{5}{3}[/tex]

y - 0 = [tex]-\frac{5}{3}(x-11)[/tex]

y = [tex]-\frac{5}{3}(x-11)[/tex]

Now satisfy this equation with the points given in the options,

Option (1)

For (1.67, -15.59),

-15.59 = [tex]-\frac{5}{3}(1.67-11)[/tex]

-15.59 = -15.55

False.

Therefore, given point doesn't lie on the line.

Option (2)

For (-0.33, -13.59)

-13.59 = [tex]-\frac{5}{3}(-0.33-11)[/tex]

-13.59 = -18.88

False

Option (3)

For (0.67, -18.59),

-18.59 = [tex]-\frac{5}{3}(0.67-11)[/tex]

-18.59 = 17.22

False

Option (4)

For (1.67, -15.59)

-15.59 = [tex]-\frac{5}{3}(1.67-11)[/tex]

-15.59 = -15.55

False.

Therefore, none of the points given in the options are lying on the line.

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