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 =(5)/(2)x -(7)/(2)`

Now on comparing to slope intercept form , we have ,

`\longrightarrow m =(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)= (-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) = (-2)/(5)(x -3)`

Open the brackets and simplify,

`\longrightarrow y +2 = (-2)/(5)x +(6)/(5)`

Subtracting 2 both sides ,

`\longrightarrow y=(-2)/(5)x +(6)/(5)-2`

`\longrightarrow y =(-2)/(5)x +(6-10)/(5)`

Simplify,

`\longrightarrow \underline{\underline{ y = (-2)/(5)x -(4)/(5)}}`

This is the required answer !