Question

The line through point ( m , -9 ) and ( 7 , m ) has slope m. The y – intercept of this line is
A) -18
B) -6
C) 6
D) 18

Answer 1

Hint: First find the slope of the line using the points through which it passes and equating it to m. On further solving the quadratic equation the value of m could be found. Find the equation of the line and put x = 0 to get the y intercept.

Complete step-by-step answer:
Let us find the slope of the given line ,
= $\left( {\dfrac{{y_2 - y_1}}{{x_2 - x_1}}} \right)$
= $\left( {\dfrac{{m - \left( { - 9} \right)}}{{7 - m}}} \right)$
= $\dfrac{{m + 9}}{{7 - m}}$
But it is given that the slope is m .
Therefore,
$\dfrac{{m + 9}}{{7 - m}}$ = m
$\Rightarrow$ $m + 9 = m\left( {7 - m} \right)$
$\Rightarrow m + 9 = 7m - {m^2}$
$\Rightarrow {m^2} - 6m - 9 = 0$
$\Rightarrow {\left( {m - 3} \right)^2} = 0$
$\Rightarrow m = 3$
Now the equation of the line $\to$
$y - y_1 = m\left( {x -x_1} \right)$
$\Rightarrow$ $y - \left( { - 9} \right) = m\left( {x - m} \right)$
Putting m = 3
$\Rightarrow$ $y + 9 = 3\left( {x - 3} \right)$
For finding the y intercept we have to put x = 0 in the above equation .
$\Rightarrow$ $y + 9 = 3\left( {0 - 3} \right)$
$\Rightarrow y + 9 = - 9$
$\Rightarrow y = - 18$
Therefore, -18 is the required y intercept.

Note: In such questions we should know the concept and formula of slope intercept from a point to get the desired answer. Remember that on putting x=0, we get the y intercept and on putting y=0, we get the x intercept.