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.

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.

-9b - z = 7b - 4z + 4
-9b = 7b - 4z + 4 + z
-9b - 7b = -4z + 4 + z
-16b = -3z + 4
b = \( \frac{-3z + 4}{-16} \)
b = \( \frac{-3z}{-16} \) + \( \frac{4}{-16} \)
b = \(\frac{3}{16}\)z - \(\frac{1}{4}\)

A circle is a figure in which each point around its perimeter is an equal distance from the center. The radius of a circle is the distance between the center and any point along its perimeter. A chord is a line segment that connects any two points along its perimeter. The diameter of a circle is the length of a chord that passes through the center of the circle and equals twice the circle's radius (2r).

To solve this equation, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)

5a(a - y)
5(-4)(-4 - 9)
5(-4)(-13)
(-20)(-13)
260

The area of a trapezoid is one-half the sum of the lengths of the parallel sides multiplied by the height:

a = ½(b + d)(h)
a = ½(8 + 9)(5)
a = ½(17)(5)
a = ½(85) = \( \frac{85}{2} \)
a = 42\(\frac{1}{2}\)