Question

write an equation in slope intercept form of the line perpendicular to the graph of 5x-2y=7 that passes through (3,-2)

Answer 1

Given :-

• A equation which is 5x - 2y = 7 .

To Find :-

• The equation of the line perpendicular to the given line and passes through (3,-2) .

Solution :-

Given equation to us is ,

$\longrightarrow 5x -2y = 7$

Convert it into slope intercept form which is y = mx + c ,

$\longrightarrow 2y = 5x - 7$

Divide both sides by 2 ,

$\longrightarrow y =\dfrac{5}{2}x -\dfrac{7}{2}$

Now on comparing to slope intercept form , we have ,

$\longrightarrow m =\dfrac{5}{2}$

And as we know that the product of slopes of two perpendicular lines is -1 . Therefore the slope of the perpendicular line will be negative reciprocal of slope of the given line . As ,

$\longrightarrow m_{\perp}= \dfrac{-2}{5}$

Again the given point to us is (3,-2) . We may use the point slope form to find out the equation of perpendicular line which is ,

$\longrightarrow y - y_1 = m(x-x_1)$

Substitute ,

$\longrightarrow y - (-2) = \dfrac{-2}{5}(x -3)$

Open the brackets and simplify,

$\longrightarrow y +2 = \dfrac{-2}{5}x +\dfrac{6}{5}$

Subtracting 2 both sides ,

$\longrightarrow y=\dfrac{-2}{5}x +\dfrac{6}{5}-2$

$\longrightarrow y =\dfrac{-2}{5}x +\dfrac{6-10}{5}$

Simplify,

$\longrightarrow \underline{\underline{ y = \dfrac{-2}{5}x -\dfrac{4}{5}}}$

This is the required answer !