Math: 30281058

ID: 30281058

(SAT Suite Question Bank > Find Questions > Assessment: SAT + Test: Math + Domain: Advanced Math)

Comment: Do not be intimidated by the extra variables. Approach the question the same way you would any other system of equations.

Method 1: A point of intersection between a line and a parabola will have the same coordinates, and the two ordered pairs happen to provide us with the x-value for both points of intersection, 1 and 5. Plug in these values to independently solve for a and b.

(a) = (1)^2 - 9

a = -8

(b) = (5)^2 - 9

b = 25 - 9

b = 16

To figure out the slope, m, of the line, divide the change in y by the change in x:

m = (16 - -8)/(5 - 1)

m = 24/4

m = 6

The correct answer is (A).

Method 2: Desmos can make quick work of the question. Graph the first equation and use the slider to determine the y-values at x = 1 and x = 5.

When x = 1, y = -8, and when x = 5, y = 16. The slope is definitely positive, so answer choices (C) and (D) are out. Then, apart from calculating the slope, you can also reason that a slope of 2 would mean that shifting right by 4 units ought to produce a corresponding y-value 8 units above -8, which would only get to 0. That point—(5, 0) is not on the parabola, which touches the x-axis on the positive side much sooner at 3. Thus, the correct answer is (A). Everything else can safely be ruled out.

Method 3: This is not really a question for which plugging in the answers makes sense because a slope describes a rate of change, and there are still two unknowns in a and b to deal with. Sure, you could set the slope equal to a given answer choice and then compare to a graph, but then why not just use the graph? Some conceptual knowledge is crucial to solving this question.