A line on the coordinate grid can be defined by a slope-intercept equation: y = mx + b. For a given value of x, the value of y can be determined given the slope (m) and y-intercept (b) of the line. The slope of a line is change in y over change in x, \({\Delta y \over \Delta x}\), and the y-intercept is the y-coordinate where the line crosses the vertical y-axis.

The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:

b² - 7b - 8 = 0
(b + 1)(b - 8) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (b + 1) or (b - 8) must equal zero:

If (b + 1) = 0, b must equal -1
If (b - 8) = 0, b must equal 8

So the solution is that b = -1 or 8

The volume of a cube is height x length x width:

v = h x l x w
v = 4 x 5 x 4
v = 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.

-3z - 5 = -2 + 3z
-3z = -2 + 3z + 5
-3z - 3z = -2 + 5
-6z = 3
z = \( \frac{3}{-6} \)
z = -\(\frac{1}{2}\)

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

c² = a² + b²
c² = 6² + 3²
c² = 36 + 9
c² = 45
c = \( \sqrt{45} \)