Question

A line goes through the points (9,8) and (4,-12). What is the slope of the line? Show your work Write the equation of the line in point-slope form. Show your work Write the equation of the line in slope-intercept form. Show your work.

Answer 1

The slope of the line is 4

The point slope form of the line can be written as (y - 8) = 4(x - 9)

The slope intercept form of the line is y = 4x - 28

In order to find the slope you will need to use the formula for slope. It is included below.

m(slope) = (y2 - y1)/(x2 - x1)

m = (8 - -12)/(9 - 4)

m = (8 + 12)/(9 - 4)

m = 20/5

m = 4

Now that we have the slope, we can plug it into point slope form along with one of the points.

(y - y1) = m(x - x1)

(y - 8) = 4(x - 9)

Now to get to the slope-intercept form of the line, we can simply manipulate the point-slope form until it is in y = mx + b

(y - 8) = 4(x - 9) ----> Distribute the 4

y - 8 = 4x - 36 -----> Add 8 to both sides

y = 4x - 28