Question

3. A line goes through the points (3,4) and (-3,6).

(a) What is the slope of the line? Show your work
(b) Write the equation of the line in point-slope form. Show your work
(c) Write the equation of the line in slope-intercept form. Show your work.

Answer 1

Part a) The slope is
`m=-(1)/(3)`

Part b) The equation in point slope form is
`y-4=-(1)/(3)(x-3)`

Part c) The equation in slope-intercept form is
`y=-(1)/(3)x+5`

Explanation:

we have the points (3,4) and (-3,6)

Part a) What is the slope of the line?

The formula to calculate the slope between two points is equal to

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

substitute the given points

`m=(6-4)/(-3-3)`

`m=(2)/(-6)`

`m=-(1)/(3)`

Part b) Write the equation of the line in point-slope form

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

we have

`m=-(1)/(3)`

`point\ (3,4)`

substitute

`y-4=-(1)/(3)(x-3)` ---> equation in point slope form

Part c) Write the equation of the line in slope-intercept form

`y=mx+b`

we have

`y-4=-(1)/(3)(x-3)`

Isolate the variable y

distribute right side

`y-4=-(1)/(3)x+1`

Adds 4 both sides

`y=-(1)/(3)x+1+4`

`y=-(1)/(3)x+5` ---> equation in slope intercept form