SQB Logo
sqbofficial

Question in-the

1.3 Linear Equations in Two Variables - Writing equations from data/points
0:00

In the xy-plane, the points with coordinates negative 2 comma 3 and 4 comma negative 5 lie on the graph of which of the following linear functions?

A.

f of x equals, x plus 5

B.

f of x equals, one half x, plus 4

C.

f of x equals, negative, four thirds x, plus one third

D.

f of x equals, negative, three halves x, plus 1

In the xy -plane, the points and lie on the graph of which of the following

Hard-difficulty · SAT Math · Linear Equations in Two Variables — Writing equations from data/points. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.

Answer explanation

Choice C is correct. A linear function can be written in the form f of x equals, m x plus b, where m is the slope and b is the y-coordinate of the y-intercept of the line. The slope of the graph can be found using the formula m equals, the fraction with numerator y sub 2 minus y sub 1, and denominator x sub 2 minus x sub 1, end fraction. Substituting the values of the given points into this formula yields m equals, the fraction with numerator negative 5 minus 3, and denominator 4 minus negative 2, end fraction or m equals, negative 8 over 6, which simplifies to m equals, negative four thirds. Only choice C shows an equation with this slope.

Choices A, B, and D are incorrect and may result from computation errors or misinterpreting the given information.

More Linear Equations in Two Variables practice questions

Browse all Heart of Algebra practice questions or return to the full SAT question bank.