PSAT Math Grid-Ins Question 50: Answer and Explanation

Question: 50

If Ax + By = C is the standard form of the line that passes through the points (-4, 1) and (3, -2),where A is an integer greater than 1, what is the value of B?

Correct Answer: 7

Explanation:

7

Difficulty: Hard

Category: Heart of Algebra/Linear Equations

Getting to the Answer: To write the equation of a line, you need two things: the slope and the y-intercept. Start by finding these, substituting them into slope--intercept form of a line (y = mx + b), and then manipulate the equation so that it is written in standard form. Use the given points, (-4, 1) and (3, -2), and the slope formula to find m:

Next, find the y-intercept, b, using the slope and one of the points:

Write the equation in slope-intercept form:

Now, rewrite the equation in the form Ax + By = C, making sure that A is a positive integer (a whole number greater than 0):

The question asks for the value of B (the coefficient of y), so the correct answer is 7.