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, 5) and (2, -1) so the slope becomes:

Plugging these values into the slope-intercept equation:

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

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

a = ½bh
a = ½ x 8 x 4 = \( \frac{32}{2} \) = 16

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 w° = 16, the value of z° is 16.

The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:

y² - 13y + 40 = 0
(y - 5)(y - 8) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (y - 5) or (y - 8) must equal zero:

If (y - 5) = 0, y must equal 5
If (y - 8) = 0, y must equal 8

So the solution is that y = 5 or 8

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.

8a - 3 < \( \frac{a}{3} \)
3 x (8a - 3) < a
(3 x 8a) + (3 x -3) < a
24a - 9 < a
24a - 9 - a < 0
24a - a < 9
23a < 9
a < \( \frac{9}{23} \)
a < \(\frac{9}{23}\)