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 multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses:

(y - 5)(y + 5)
(y x y) + (y x 5) + (-5 x y) + (-5 x 5)
y² + 5y - 5y - 25
y² - 25

To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.

7a⁹ - 2a⁹ = 5a⁹

The area of a triangle is equal to ½ base x height:

a = ½bh
a = ½ x 3 x 6 = \( \frac{18}{2} \) = 9

You need to find the value of c so solve the first equation in terms of y:

9c + y = -8
y = -8 - 9c

then substitute the result (-8 - 9c) into the second equation:

7c + 9(-8 - 9c) = 8
7c + (9 x -8) + (9 x -9c) = 8
7c - 72 - 81c = 8
7c - 81c = 8 + 72
-74c = 80
c = \( \frac{80}{-74} \)
c = -1\(\frac{3}{37}\)