Question

What is the equation of the line that passes through
(-5, 0) and (4, 3)?

Answer 1

`y=(1)/(3)x+(5)/(3)`

Explanation:

The point-slope form of an equation for a line is y = mx + b (m is the slope; b is the y-intercept).

First, find the slope using the two given points.

`m=(y_2 - y_1)/(x_2-x_1)=(3-0)/(4-(-5))=(3)/(9)=(1)/(3)`

At this stage, you know the slope and need to find the y-intercept. Plug in one of the points (either one) into the equation. Let's use (-5, 0).

`y=(1)/(3)x+b\\0=(1)/(3)(-5)+b\\0=-(5)/(3)+b\\(5)/(3)=b`

The equation for the line is
`y=(1)/(3)x+(5)/(3)`.

You can check for errors by putting in the point you didn't use...

Check to make sure the point (4, 3) satisfies the equation.

`3=(1)/(3)(4)+(5)/(3)\\3=(4)/(3)+(5)/(3)\\3=(9)/(3)` True!