For parallel lines with a transversal, the following relationships apply:

• angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°)
• alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°)
• all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other
• same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°)

Applying these relationships starting with b° = 157, the value of y° is 157.

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.

6a x 4b = (6 x 4) (a x b) = 24ab

When solving an equation with two variables, 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.)

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.

-7b + 5y = -9b + 7y + 7
-7b = -9b + 7y + 7 - 5y
-7b + 9b = 7y + 7 - 5y
2b = 2y + 7
b = \( \frac{2y + 7}{2} \)
b = \( \frac{2y}{2} \) + \( \frac{7}{2} \)
b = y + 3\(\frac{1}{2}\)

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, 5) so the slope becomes: