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

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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

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