Question

Which equation represents the line that passes through (–8, 11) and (4, 7/2)?

Answer 1

Answer:

Option A -  $y=-\frac{5}{8}x+6$

Step-by-step explanation:

Given : Two points $(-8, 11)$ and $(4,\frac{7}{2})$

To find : The equation represent the line

Solution :

The general form of the equation is $(y-y_1)=m(x-x_1)$

Where, m is the slope of the equation

First we find the slope of the equation $m=\frac{y_2-y_1}{x_2-x_1}$

$(x_1,y_1)=(-8,11)$ and  $(x_2,y_2)=(4,\frac{7}{2})$

Substitute the value,

$m=\frac{\frac{7}{2}-11}{4-(-8)}$

$m=\frac{\frac{-15}{2}}{12}$

$m=-\frac{5}{8}$

Slope of the equation is $m=-\frac{5}{8}$

Now, Take any point let $(x_1,y_1)=(-8,11)$

The equation form is  $(y-11)=-\frac{5}{8}(x-(-8))$

$y-11=-\frac{5}{8}(x+8)$

$y-11=-\frac{5}{8}x-5$

$y=-\frac{5}{8}x+6$

Therefore, Option A is correct.

The required equation is $y=-\frac{5}{8}x+6$

Answer 2

Answer: First option: y = -5/8x + 6