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1.3 Linear Equations in Two Variables - Graphing two-variable lines
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a, x, plus b y, equals b

In the equation above, a and b are constants and 0 is less than a, which is less than b. Which of the following could represent the graph of the equation in the xy-plane?

A.

 

The answer choice presents the graph of a line in the x y-plane. The number 1 is indied on both axes. The line slants downward and to the right, crossing the y axis at 1, and crossing the x axis at 1.

 

B.

 

The answer choice presents the graph of a line in the x y-plane. The number 1 is indied on both axes. The line slants downward and to the right, crossing the x axis at negative 1, and crossing the y axis at negative 1.

 

C.

 

The answer choice presents the graph of a line in the x y-plane. The number 1 is indied on both axes. The line slants downward and to the right, crossing the y axis at 1, and crossing the x axis at 2.

 

D.

 

The answer choice presents the graph of a line in the x y-plane. The number 1 is indied on both axes. The line slants downward and to the right, crossing the y axis at 1, and crossing the x axis at 0 point 5.

 

In the equation above, a and b are constants and . Which of the following could

Hard-difficulty · SAT Math · Linear Equations in Two Variables — Graphing two-variable lines. 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. The given equation a, x plus b y, equals b can be rewritten in slope-intercept form, y equals, m x plus k, where m represents the slope of the line represented by the equation, and k represents the y-coordinate of the y-intercept of the line. Subtracting ax from both sides of the equation yields b y equals, negative a, x plus b, and dividing both sides of this equation by b yields y equals, the negative of the fraction a over b, end fraction, times x, plus, the fraction b over b, end fraction, or y equals, the negative of the fraction a over b, end fraction, times x, plus 1. With the equation now in slope-intercept form, it shows that k equals 1, which means the y-coordinate of the y-intercept is 1. It’s given that a and b are both greater than 0 (positive) and that a is less than b. Since m equals, the negative of the fraction a over b, the slope of the line must be a value between negative 1 and 0. Choice C is the only graph of a line that has a y-value of the y-intercept that is 1 and a slope that is between negative 1 and 0.

Choices A, B, and D are incorrect because the slopes of the lines in these graphs aren’t between negative 1 and 0.

 

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