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A representation of a linear equation in two variables is graphed on the coordinate plane below. Which linear equation in two variables can be used to represent the line?

A. y = 5/2x – 3
B. y = 2/5x + 1
C. y = 2/5x - 3
D. 5x - 2y = -6

1 Answer

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Final answer:

Without seeing the graph, we compare the provided options to the standard linear equation form y = b + mx, where b is the y-intercept and m is the slope. Each option represents a different slope and y-intercept. The correct equation can be determined by matching these two elements with the graph in question.

Step-by-step explanation:

To find which linear equation in two variables corresponds to the graphed line, we need to know the slope and the y-intercept. If a graph is provided, these two elements can be determined visually from the graph. As we know from the given instruction materials, a linear equation is commonly expressed in the form y = b + mx, where b is the y-intercept and m is the slope. The slope indicates how steep the line is and the y-intercept is where the line crosses the y-axis.

Without the actual graph, we cannot visually determine the slope and y-intercept. However, if the choice must be made from the given options, we compare their format to the standard linear equation form. Option A (y = 5/2x – 3) implies a slope of 5/2 and a y-intercept of -3. Option B (y = 2/5x + 1) has a slope of 2/5 and a y-intercept of +1. Option C (y = 2/5x – 3) also has a slope of 2/5 but a y-intercept of -3. Option D (5x – 2y = -6) can be rearranged to y = 5/2x + 3, with a slope of 5/2 and y-intercept of 3.

To determine the correct equation, the student would need to graph the equations or assess the given line for its slope and y-intercept, matching it with the correct equation from the choices.

User Samuel Hsieh
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