Question

What is the equation in slope intercept form of the line that passes through the point

(2,-2) and is perpendicular to the line represented by y= 1/4x+ 2?​

Answer 1

The equation of the second line perpendicular;ar to the given line

is y + 4x = 6

Explanation:

Here, the equation of line is :
`y = (1)/(4) x + 2`

The general slope intercept form of any equation is

(y - y0) = m(x-x0) : here, m = slope of the given line.

So, by comparing this to equation 1,

slope m 1 = (1/4)

Now, given the next line is perpendicular to the first line.

If two lines are perpendicular to each other with respective slopes m 1 and m 2, then ( m 1 x m 2) = -1

So, the slope of the second line = -1/m1

or, m2 = -4

The gicen point on the second line is (2,-2)

so, by SLOPE INTERCEPT FORM of an equation:

(y-(-2)) = (-4)(x -2)

OR, y + 2 = -4x + 8

Hence, the equation of the second line is y + 4x = 6