Question

Write the equation of the line that passes through the points (4, -3) and (-5, 4).

Answer 1

Answer:

y₁ - y₂ = (-7/9)(x₁ - x₂)

Step-by-step explanation:

The general structure for an equation in point-slope form is:

y₁ - y₂ = m(x₁ - x₂)

In this form, "m" represents the slope and the "x" and "y" values come from each point. To find "m", plug the values of each point into the equation.

Point 1: (4, -3)                   Point 2: (-5,4)

y₁ - y₂ = m(x₁ - x₂)                                  <---- Original equation

-3 - 4 = m(4 - (-5))                                 <---- Plug values in for "x" and "y"

-7 = m(4 - (-5))                                      <---- Simplify left side

-7 = m(9)                                               <---- Simplify within parentheses

-7/9 = m                                              <---- Divide both sides by 9

I don't exactly understand what "fully simplified point-slope form" means because if all of the variables are plugged in, you wouldn't be left with an equation. It may just be asking for the slope, which in this case would make the equation look like this:

y₁ - y₂ = (-7/9)(x₁ - x₂)  

It may want you to find the equation in slope-intercept form (y = mx + b), and you would have to find "b". Sorry I don't quite understand what exactly you are looking for.