Question

Find the equation of a line that contains the points (3,7) and (-6, 4). Write the equation in slope-intercept form, using

fractions when required.

Answer 1

`y=(1)/(3) x+6`

Explanation:

`(3,7)(-6,4)`

Step 1. Find the slope (by using the slope-formula)

m = slope

`m=(y_2-y_1)/(x_2-x_1)`

`m=(4-7)/(-6-3)`

`m=(-3)/(-9)`

`m=(3)/(9)`

`m=(1)/(3)`

Step 2. Write the equation (using the slope and the points)

Here's how to do it:

Slope-intercept Formula
`y=mx+b` whrere m = slope and b = y-intercept

Plug in the slope into the Slope-intercept Formula

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

Find the y-intercept (b) by using a point and substituting their x and y values

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

Point: (3, 7)

`7=(1)/(3) (3)+b`

`7=1+b`

`b=7-1`

`b=6`

Step 3. Write the equation in Slope-intercept form

`y=mx+b`

`y=(1)/(3) x+6`