Question

A line passes through the point (4,–2) and is perpendicular to the line with the equation y = 2⁄3x + 4. What's the equation of the line?

Answer 1

Answer:

y= -3/2x + 1

Step-by-step explanation:

The slope of this line is 2/3. The slope of the line perpendicular to this line will be the negative reciprocal or -3/2.

Write the equation using the slope m=-3/2 and the point slope form.

$y-y_1=m(x-x_1)\\y--2=-\frac{3}{2}(x-4)\\y+2=-\frac{3}{2}(x-4)$

This is the equation of the line. You can convert it to slope intercept form:

$y+2=-\frac{3}{2}(x-4)\\y+2 = -\frac{3}{2}x + 3\\y=-\frac{3}{2}x +1$