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.
