2. m = 1/2. Lines that are parallel to each other have the same slope.
3. m = 4
First, find the slope of the original line using (y₂-y₁)/(x₂-x₁)
(-13 + 5)/(15 + 17) = -1/4
Lines that are perpendicular to each other have slopes that are the negative reciprocals of each other. So basically, flip the -1/4 into -4/1 and make it positive which results in m = 4.
4. m = -4/5. As I mentioned before, lines that are parallel to each other have the same slope.
5. m = -1. Find the negative reciprocal of 1 since the lines are perpendicular.
6. m = 1/3. Find the negative reciprocal of -3 since the lines are perpendicular.
7. m = -1
Find the slope by using (y₂-y₁)/(x₂-x₁)
(-16 + 10)/(8 - 2) = -1. Since the lines are parallel, the slopes are the same.
8. m = 10/3
Get the equation in the form y = mx+b
3y = 10x - 3
Divide the entire equation by 3
y = (10/3)x - 1.
10/3 is in the place of m, so m = 10/3. Since the lines are parallel, the slopes are the same.
9. m = -5/6
Get the equation in the form of y = mx+b
6x - 5y = 11
Subtract 6x on both sides
-5y = 11 - 6x
Divide the entire equation by -5
y = (-11/5) + (6/5)x
Now rearrange the equation
y = (6/5)x - 11/5
6/5 is in the place of m, so m = 6/5. Since the lines are perpendicular to each other, find the negative reciprocal of 6/5 which is -5/6.
10. m = 1/7
The equation is already in the form of y = mx+b, and we can see that -7 is in place of m. Since the lines are perpendicular to each other, find the negative reciprocal of -7 which is 1/7.