What is the equation of a slope intercept line through the points of (0,-2) and (3,-4)

Question

What is the equation of a line ,using slope intercept form, that passes through these two point pairs? (0,-2) and (3,-4).

Answer 1

Hi Mara, we can solve this problem using the following steps:

 

Step 1: find the slope of the line through the two given points

 

Step 2: find the point-slope form of the line given the slope from step 1 and one of the two given points. It does not matter which of the two points is selected.

 

Step 3: convert the point-slope form of the line to the slope-intercept form of the line.

 

Step 1: the slope of a line can be determined by the change in rise divided by the change in run.

 

Change in rise:

 

Use the two y-values to get the change in rise.

 

-2 - (-4) = 2, or the change in rise.

 

Change in run:

 

Use the two x-values to get the change in run.

 

0 - 3 = -3, or the change in run

 

The slope of the line through the two given points equals -2/3.

 

Step 2: the point-slope of the line is given by the equation, y - y₁ = m * (x - x₁)

 

m = -2/3

 

Let x₁ = 0 and y₁ = -2, remember, it does not matter which of the two given points are used in this step.

 

Substituting gives:

 

y - (-2) = -2/3 * (x - 0)

 

y + 2 = -2/3 * x

 

Step 3: the slope-intercept form of the line is: y = m * x + b.

 

We have y + 2 = -2/3 * x, which is almost the slope-intercept form of the line.

 

Subtract 2 from both sides of the equation gives:

 

y = -2/3 * x - 2, which is in the slope-intercept form of the line.