Answer:
The equation of the line perpendicular to the line
-2x + 4y = 6
and passing through (-3, 4) is:
Step-by-step explanation:
Given the line:
-2x + 4y = 6 .............................................................................(1)
To find the equation of the line that is perpendicular to (1), we need to rewrite (1) in slope-intercept form.
Add 2x to both sides of (1)
4y = 2x + 6
Divide both sides by 4
y = (2/4)x + 6/4
y = (1/2)x + 3/2 ......................................................................(2)
Where 1/2 is the slope, and 3/2 is the y-intercept.
An equation perpendicular to (2) has it's slope as the negative reciprocal of (2). It is in the form:
y = -2x + b ..........................................................................(3)
Since this line passes through (-3, 4), put x = -3, and y = 4 in (3)
4 = (-2)(-3) + b
4 = 6 + b
Subtract 6 from both sides
b = 4 - 6 = -2
Using b = -2 in (3), we have:
y = -2x - 2