Parallel and Perpendicular Lines

Question

Write an equation in slope-intercept form for the line that is perpendicular to y= -1/4x + 2 and passes through the point (-4, 3).

Answer 1

Hi, Tamika!

The equation of the line given to us is in slope intercept form : y = mx + b where "m" is our slope. So since -1/4 is in the "m" spot, we know the slope of the line given is -1/4.

Now, we are looking for a line perpendicular to the equation given. Perpendicular lines have what we call "opposite reciprocal" slopes. Opposite refers to the positive/negative sign and reciprocal means it's flipped. So the opposite reciprocal of the given -1/4 slope would be +4/1 or just 4. We can now plug this 4 in for m in the slope intercept form:

y = 4x + b

Now, we need to find our "b" which stands for y-intercept. To do this, we plug in the point they give us for x and y and then solve for b:

y = 4x + b

3 = 4(-4) + b

3 = -16 + b

+16

19 = b

So our y-intercept is 19. We can plug this into the slope intercept equation to get our final answer:

y = 4x + 19

I hope this explanation was thorough and answered all of your questions. If you have any confusion on any step, please don't hesitate to reach out. Learn on! :)

Answer 2

The slopes of perpendicular lines are opposite reciprocals, so the slope of our perpendicular line would be m=4. Now we take the point given and the slope m=4, and we plug them into the point slope formula:

y - y₁ = m(x - x₁) → y - 3 = 4(x - -4) → y - 3 = 4(x + 4)

Now, we distribute the four into the parenthesis to get:

y - 3 = 4x + 16

Finally, we add 3 to both sides to get:

y =4x + 19