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, 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.

6y - 5 = \( \frac{y}{6} \)
6 x (6y - 5) = y
(6 x 6y) + (6 x -5) = y
36y - 30 = y
36y - 30 - y = 0
36y - y = 30
35y = 30
y = \( \frac{30}{35} \)
y = \(\frac{6}{7}\)

An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite:

d° = b° + c°

To find angle c, remember that the sum of the interior angles of a triangle is 180°:

180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 20° - 23° = 137°

So, d° = 23° + 137° = 160°

A shortcut to get this answer is to remember that angles around a line add up to 180°:

a° + d° = 180°
d° = 180° - a°
d° = 180° - 20° = 160°

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

-6a - 8x = -3a + 6x + 9
-6a = -3a + 6x + 9 + 8x
-6a + 3a = 6x + 9 + 8x
-3a = 14x + 9
a = \( \frac{14x + 9}{-3} \)
a = \( \frac{14x}{-3} \) + \( \frac{9}{-3} \)
a = -4\(\frac{2}{3}\)x - 3

To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.

(5a)(5ab) - (9a²)(8b)
(5 x 5)(a x a x b) - (9 x 8)(a² x b)
(25)(a¹⁺¹ x b) - (72)(a²b)
25a²b - 72a²b
-47a²b