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Algebra / Linear equations in two variables Difficulty: Easy

The figure presents the graph of a line in the x y plane. The number 1 is indicated on both axes. The line passes through the point with coordinates negative 4 comma 0, and the point with coordinates 0 comma negative 1.

Which of the following is an equation of the graph shown in the xy-plane above?

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Explanation

Choice A is correct. The slope of the line can be found by choosing any two points on the line, such as (4, –2) and (0, –1). Subtracting the y-values results in –2 – (–1) = –1, the change in y. Subtracting the x-values results in 4 – 0 = 4, the change in x. Dividing the change in y by the change in x yields $negative 1, divided by 4, equals negative one fourth$ , the slope. The line intersects the y-axis at (0, –1), so –1 is the y-coordinate of the y-intercept. This information can be expressed in slope-intercept form as the equation $y equals, negative one fourth, x, minus 1$ .

Choice B is incorrect and may result from incorrectly calculating the slope and then misidentifying the slope as the y-intercept. Choice C is incorrect and may result from misidentifying the slope as the y-intercept. Choice D is incorrect and may result from incorrectly calculating the slope.