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1.3 Linear Equations in Two Variables - Writing equations from data/points
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The figure presents a graph of a line in the x y-plane with the origin labeled O. The numbers negative five through positive five are indied along the x- and y-axes. The line begins in the second quadrant and moves downward and to the right. It crosses the y-axis at 3 and the x-axis at one.

What is the equation of the line shown in the xy-plane above?

A.
y equals 3 x minus 3
B.
y equals negative 3 x plus 3
C.
y equals one-third x minus 3
D.
y equals negative one-third x plus 3

What is the equation of the line shown in the xy -plane above?

Medium-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 B is correct. Any line in the xy-plane can be defined by an equation in the form y = mx + b, where m is the slope of the line and b is the y-coordinate of the y-intercept of the line. From the graph, the y-intercept of the line is (0, 3). Therefore, b = 3. The slope of the line is the change in the value of y divided by the change in the value of x for any two points on the line. The line shown passes through (0, 3) and (1, 0), so m equals, the fraction with numerator 3 minus zero, and denominator zero minus 1, or m = –3. Therefore, the equation of the line is y = –3x + 3.

Choices A and C are incorrect because the equations given in these choices represent a line with a positive slope. However, the line shown has a negative slope. Choice D is incorrect because the equation given in this choice represents a line with slope of negative one third. However, the line shown has a slope of  –3.

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