Question

Write an equation in slope-intercept form for the line that passes through the point  ( -1 , -2 )  and is perpendicular to the line − 4 x − 3 y  =  − 5

Answer 1

The equation in slope-intercept form for the line that passes through the point ( -1 , -2 ) and is perpendicular to the line − 4 x − 3 y = − 5 is
`y = (3)/(4)x - (5)/(4)`

Solution:

The slope intercept form is given as:

y = mx + c ----- eqn 1

Where "m" is the slope of line and "c" is the y - intercept

Given that the line that passes through the point ( -1 , -2 ) and is perpendicular to the line − 4 x − 3 y = − 5

Given line is perpendicular to − 4 x − 3 y = − 5

− 4 x − 3 y = − 5

-3y = 4x - 5

3y = -4x + 5

`y = (-4x)/(3) + (5)/(3)`

On comparing the above equation with eqn 1, we get,

`m = (-4)/(3)`

We know that product of slope of a line and slope of line perpendicular to it is -1

`(-4)/(3) * \text{ slope of line perpendicular to it}= -1\\\\\text{ slope of line perpendicular to it} = (3)/(4)`

Given point is (-1, -2)

Now we have to find the equation of line passing through (-1, -2) with slope
`m = (3)/(4)`

Substitute (x, y) = (-1, -2) and m = 3/4 in eqn 1

`-2 = (3)/(4)(-1) + c\\\\-2 = (-3)/(4) + c\\\\c = - 2 + (3)/(4)\\\\c = (-5)/(4)`

`\text{ substitute } c = (-5)/(4) \text{ and } m = (3)/(4) \text{ in eqn 1}`

`y = (3)/(4) * x + (-5)/(4)\\\\y = (3)/(4)x - (5)/(4)`

Thus the required equation of line is found