Math: fdee0fbf

ID: fdee0fbf

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

Comment: Linear modeling 101. The only potential challenge is the extra variable.

Method 1: We need to find a particular y-value that lies on a line. We know the y-intercept, (0, -6), and an additional point in its entirety, (2, 2), allowing us to model the line and solve for the unknown w. Note that we do not even need to work through m = (y2 - y1)/(x2 - x1), since we can solve for the slope algebraically using the other values we already know.

y = mx + b

y = mx + (-6)

(2) = m(2) - 6

8 = 2m

4 = m

y = 4x - 6

Plug in the point (20, w).

(w) = 4(20) - 6

w = 80 - 6

w = 74

The correct answer must be 74.

Method 2: Although it might be faster to simply work out the algebraic solution, there is nothing wrong with graphing the linear equation y = 4x - 6 above and checking for the y-value when x = 20. As I have done in the past on other questions, I am going to show how to reveal the answer in a table. Click on the "gear" icon above the equation to Edit List. Delete everything except for two inputs, since the y-value generates automatically: x = 0 and x = 20.

The correct answer is in plain sight, and w must be 74. You could, alternatively, add a second equation, x = 20, and look for the point of intersection.

The point is, if you have Desmos at your fingertips, why not use it to your advantage? If organizational mistakes pop up now and then when you derive an answer algebraically, it may be in your best interest to learn to graph and look for solutions instead.

Method 3: If you work more mechanically when modeling a line and have grown accustomed to deriving a slope from two points, the question may take slightly more time, but the result will be the same.

y = mx + b

y = mx + (-6)

y = mx - 6

m = ((2) - (-6))/((2) - (0))

m = 8/2

m = 4

y = 4x - 6

(w) = 4(20) - 6

w = 80 - 6

w = 74

The correct answer is 74.