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 -1. 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:

Plugging these values into the slope-intercept equation:

y = -2x - 1

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(7 + 5)(4)
a = ½(12)(4)
a = ½(48) = \( \frac{48}{2} \)
a = 24

You need to find the value of b so solve the first equation in terms of x:

-5b + x = -6
x = -6 + 5b

then substitute the result (-6 - -5b) into the second equation:

9b - 3(-6 + 5b) = 5
9b + (-3 x -6) + (-3 x 5b) = 5
9b + 18 - 15b = 5
9b - 15b = 5 - 18
-6b = -13
b = \( \frac{-13}{-6} \)
b = 2\(\frac{1}{6}\)

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:

To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.

2a⁶ - 5a⁶ = -3a⁶