Jim J. answered • 10/24/23
Certified, highly experienced tutor of Geometry.
Hi Jayli,
When we are trying to find the equation of a line, we need two things: any point and the slope. We have been given the point (-4, 11). To find the slope, we are going to use the other line given to help us find it. We know that if two lines are perpendicular, their slopes are opposite reciprocals. For example, if one line has a slope of 2, a line perpendicular to this line has a slope of -1/2. Notice that if I find the reciprocal of 2, that is 1/2. Then, change the sign. -1/2. Easy, right!
The line we are given is y = (1/4)x - 3. To find the slope of a perpendicular line, turn 1/4 upside down and change the sign. So, -4/1 or simply -4.
Now, we are ready to find the equation of the line we are looking for. We have the point (-4, 11) and the slope -4.
The equation of the line has the form y = mx + b. (Notice there are four letters: y, m, x, and b. We have three of them: an x-coordinate, a y-coordinate, and the slope m. We can find the b.
Substituting, we see that . . .
y = mx + b
11 = -4(-4) + b
11=16 + b
-5 = b
So, the equation of the line we are looking for is y = -4x - 5
Hope this helps!
:)
