We are given the point (-3,2). We want the equation of the line that passes through this point and that is perpendicular to the line 2x-4y=10.
First, to solve this problem, we will write the given line equation in the slope -intercept form That is:
we subtract 10 on both sides to get
now, we add 4y on both sides to get
Finally we divide both sides by 4, so we get
from this equation, we can see that the slope of the given line is 1/2.
Now, to calculate the line we will use the following fact. The product of the slopes of two perpendicullar lines is -1.
Let m be the slope of the line we are looking for. Due to this fact we have the equation
so if we multiply both sides by 2, we get that
so now we know that the slope of the line should be -2.
So we know that the slope is -2 and that is passes through the point (-3,2). Then, we use this formula
where (x0,y0) is the point through which the liness passes. That is, in our case (-3,2). So we get
now we add 2 on both sides, so we get
if we distribute the product, we get
so the equation of the line is y=-2x-4