Question

Write the equation of the line that passes through

the points (-1, 2) and (6, 3) in slope-intercept form.

Answer 1

`y=(\displaystyle 1)/(\displaystyle 7)x+(\displaystyle15)/(\displaystyle 7)`

Explanation:

Hi there!

Slope-intercept form:
`y=mx+b` where m is the slope and b is the y-intercept (the value of y when x is 0)

1) Determine the slope (m)

`m=(\displaystyle y_2-y_1)/(\displaystyle x_2-x_1)` where two given points are
`(x_1,y_1)` and
`(x_2,y_2)`

Plug in the given points (-1, 2) and (6, 3):

`m=(\displaystyle 3-2)/(\displaystyle 6-(-1))\\\\m=(\displaystyle 3-2)/(\displaystyle 6+1)\\\\\m=(\displaystyle 1)/(\displaystyle 7)`

Therefore, the slope of the line is
`(\displaystyle 1)/(\displaystyle 7)`. Plug this into
`y=mx+b`:

`y=(\displaystyle 1)/(\displaystyle 7)x+b`

2) Determine the y-intercept (b)

`y=(\displaystyle 1)/(\displaystyle 7)x+b`

Plug in one of the given points and solve for b:

`2=(\displaystyle 1)/(\displaystyle 7)(-1)+b\\2=-(\displaystyle 1)/(\displaystyle 7)+b`

Add
`(\displaystyle 1)/(\displaystyle 7)` to both sides to isolate b:

`2+(\displaystyle 1)/(\displaystyle 7)=-(\displaystyle 1)/(\displaystyle 7)+b+(\displaystyle 1)/(\displaystyle 7)\\\\(\displaystyle15)/(\displaystyle 7) =b`

Therefore, the y-intercept of the line is
`(\displaystyle15)/(\displaystyle 7)`. Plug this back into
`y=(\displaystyle 1)/(\displaystyle 7)x+b`:

`y=(\displaystyle 1)/(\displaystyle 7)x+(\displaystyle15)/(\displaystyle 7)`

I hope this helps!