Line passing through: (-2,4) and (3,0)

Question

Line passing through: (-2,4) and (3,0)

List the coordinates of any y-intercept and the coordinates of any x-intercept. 9x-2y=36

Answer 1

Hi Julia, to find the line passing through two points, start by finding the slope. The slope is given by the rise divided by the run, or the change in y values divided by the change in x values.

 

Let m represent the slope:

 

m = (y₂ - y₁) / (x₂ - x₁)

 

m = (4 - 0) / (-2 - 3)

 

m = 4 / -5

 

Next use the point-slope equation to find the line:

 

y - y₁ = m * (x - x₁)

 

It does not matter which of the two points is used to solve this equation. 

 

Substitute for y₁, x₁, and m:

 

y - 4 = (4 / -5) * (x  - (-2))

 

multiply by -5 to clear the fraction:

 

-5y + 20 = 4 * (x + 2)

 

-5y + 20 = 4x + 8

 

In standard form, the line is:

 

-4x - 5y = -12

 

Multiply by -1:

 

4x + 5y = 12

 

For the second part, to find the x- and y-intercepts, first set y = 0 and solve for x. Then set x = 0 and solve for y.

 

y = 0, 9x = 36, x = 4

 

x = 0, -2y = 36, y = -18

 

The x-intercept is 4, and the y-intercept is -18.

 

Questions?