MTH1010_04_02_2

Question

MTH1010_04_02_2

BlackTom AI · Accepted Answer

Let’s parse the problem carefully and examine what each option implies about the line.
Option (a): It states a slope m = 5 and a y-intercept corresponding to the point (0, -2). A line with slope 5 and passing through (0, -2) has equation y = 5x - 2. If you plug in x = 0, you get y = -2, which does not match the given point (0, -5) that the problem identifies as on the line. Therefore, this option is inconsistent with the necessary intercept at x = 0.
Option (b): Here the slope is again m = 5, but the intercept is given as (0, 2). The equation would be y = 5x + 2. Evaluating at x = 0 yields y = 2, not -5, so this choice cannot describe the same line that contains (0, -5).
Option (c): This option claims m = 2 and the y-intercept is at (0, -5). A line with slope 2 through (0, -5) has equation y = 2x - 5. Indeed, when x = 0, y = -5, matching the intercept, and the slope 2 is consistent with the linear relationship y = 2x - 5.
Option (d): It asserts m = 2 and a y-intercept at (0, 5). That would give the equation y = 2x + 5. At x = 0, y = 5, which contradicts the required intercept of -5, so this does not describe the same line.
In summary, options (a), (b), and (d) all conflict with the needed y-intercept of -5 while option (c) aligns both the slope and the intercept correctly to produce y = 2x - 5. Therefore, the only option that fits the information is the one describing slope 2 with y-intercept -5.

MTH1010_04_02_2

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