The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, -3) and (2, 3) so the slope becomes:

According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:

c² = a² + b²
c² = 8² + 4²
c² = 64 + 16
c² = 80
c = \( \sqrt{80} \)

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.

3a + 5 = \( \frac{a}{-8} \)
-8 x (3a + 5) = a
(-8 x 3a) + (-8 x 5) = a
-24a - 40 = a
-24a - 40 - a = 0
-24a - a = 40
-25a = 40
a = \( \frac{40}{-25} \)
a = -1\(\frac{3}{5}\)

To solve this equation, isolate the variable for which you are solving (b) on one side of the equation and put everything else on the other side.

b + 7x = 4b + 5x - 3
b = 4b + 5x - 3 - 7x
b - 4b = 5x - 3 - 7x
-3b = -2x - 3
b = \( \frac{-2x - 3}{-3} \)
b = \( \frac{-2x}{-3} \) + \( \frac{-3}{-3} \)
b = \(\frac{2}{3}\)x + 1

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the < sign and the answer on the other.

5z - 5 < \( \frac{z}{5} \)
5 x (5z - 5) < z
(5 x 5z) + (5 x -5) < z
25z - 25 < z
25z - 25 - z < 0
25z - z < 25
24z < 25
z < \( \frac{25}{24} \)
z < 1\(\frac{1}{24}\)