Question

Find the value of r so the line passes through (r,-2) and (-7,-1) has a slope of m=-1/4

Answer 1

The value of "r" is -3 so the line passes through (r,-2) and (-7,-1) has a slope of m = -1/4

Solution:

Given that line passes through (r, -2) and (-7, -1) has a slope of
`m = (-1)/(4)`

To find: value of r

The slope of line passing through two points
`(x_1, y_1)` and
`(x_2, y_2)` is given as:

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

Here given that slope
`m = (-1)/(4)`

`\text {Also } x_(1)=r ; y_(1)=-2 ; x_(2)=-7 ; y_(2)=-1`

Substituting the values in above formula, we get

`\begin{array}{l}{m=(-1-(-2))/(-7-r)} \\\\ {(-1)/(4)=(-1+2)/(-7-r)}\end{array}`

`\begin{array}{l}{(-1)/(4)=(1)/(-7-r)} \\\\ {7+r=4} \\\\ {r=-3}\end{array}`

Thus the value of "r" is -3