Question

Wendy thinks a line that passes through the points (-4, -5) and (5, 4) also goes through the origin. Is she correct?

Answer 1

To solve this problem, first, we will determine the equation of the line that passes through those points, then we will take that equation to its slope-intercept form

$y=mx+b,$

if b is equal to zero, then the line passes through the origin.

To determine the equation of a line that passes through (x₁,y₁) and (x₂,y₂) we use the following formula:

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x_2-x_1)\text{.}$

Substituting the given points in the above formula, we get:

$y-4=\frac{-5-4}{-4-5}(x-5)\text{.}$

Simplifying the above equation, we get:

$y-4=\frac{-9}{-9}(x-5)=x-5.$

Taking the equation to its slope-intercept form we get:

$y=x-1.$

Since

$b\ne-1,$

then the line does not pass through the origin.

Answer: She is not correct.