Question

What is the slope-intercept form of the line passing through `(-2, -1)` and `(-1, 7)`?

Answer 1

`y=8x+15`

Explanation:

The slope-intercept form of a line can be represented by the equation:

`y=mx+b`

Start by finding the slope of the line, which can be calculated with the formula:

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

where:
`m=`slope
`(x_1, y_1)=(-2, -1)`
`(x_2, y_2)=(-1, 7)`

Substitute your known values into the equation to find the slope:

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

`m=(7-(-1))/(-1-(-2))`

`m=8/1`

`m=8`

So far, our equation is `y=8x+b`. We still need to find `b`, so substitute either point, `(-2,-1)` or `(-1,7)` into the equation since they are both points on the line, to find `b`. In this case, we will use `(-2,-1)`:

`y=8x+b`

`-1=8(-2)+b`

`-1=-16+b`

`b=15`

Substitute the calculated values to obtain the equation:

`y=8x+15`