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 + 3)(y + 9)
(y x y) + (y x 9) + (3 x y) + (3 x 9)
y² + 9y + 3y + 27
y² + 12y + 27

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 < sign and the answer on the other.

7a - 7 < \( \frac{a}{4} \)
4 x (7a - 7) < a
(4 x 7a) + (4 x -7) < a
28a - 28 < a
28a - 28 - a < 0
28a - a < 28
27a < 28
a < \( \frac{28}{27} \)
a < 1\(\frac{1}{27}\)

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 slope-intercept equation for a line is y = mx + b where m is the slope and b is the y-intercept of the line. From the graph, you can see that the y-intercept (the y-value from the point where the line crosses the y-axis) is 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, 1) so the slope becomes:

Plugging these values into the slope-intercept equation:

y = -\(\frac{1}{2}\)x + 2

The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c²) is equal to the sum of the two perpendicular sides squared (a² + b²): c² = a² + b² or, solved for c, \(c = \sqrt{a + b}\)