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, 0) and (2, 4) so the slope becomes:

Plugging these values into the slope-intercept equation:

y = 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, \(c = \sqrt{a + b}\)

The entire length of this line is represented by AD which is AB + BD:

AD = AB + BD

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

y² - 3y - 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

The area of a trapezoid is one-half the sum of the lengths of the parallel sides multiplied by the height:

a = ½(b + d)(h)
a = ½(4 + 7)(5)
a = ½(11)(5)
a = ½(55) = \( \frac{55}{2} \)
a = 27\(\frac{1}{2}\)