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=(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=(-5-4)/(-4-5)(x-5)\text{.}`

Simplifying the above equation, we get:

`y-4=(-9)/(-9)(x-5)=x-5.`

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

`y=x-1.`

Since

`b\\e-1,`

then the line does not pass through the origin.

Answer: She is not correct.