Question

Find an equation of the line that contains the given pair of points. ​(negative 4 ​, 7 ​), ​(minus 2​,minus7 ​) The equation of the line is nothing.

Answer 1

`y=-7x-21`

Explanation:

We have been given two points on a line as
`(-4,7)` and
`(-2,-7)`. We are asked to find the equation of the line passing through these points.

We will write our equation in slope-intercept form
`y=mx+b`, where m represents slope of line and b represents the y-intercept.

Let us find slope of line using our given points as:

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

`m=(-7-7)/(-2-(-4))`

`m=(-14)/(-2+4)`

`m=(-14)/(2)`

`m=-7`

Now, we will substitute
`m=-7` and coordinates of point
`(-4,7)` in slope-intercept form of equation as:

`7=-7(-4)+b`

`7=28+b`

`7-28=28-28+b`

`-21=b`

Substitute
`-21=b` and
`m=-7` in slope-intercept form of equation:

`y=-7x-21`

Therefore, our required equation would be
`y=-7x-21`.