#2 Which of the following are true statements about the graph of y - 4 = -\frac{1}{2}(x + 2)?

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#2 Which of the following are true statements about the graph of y - 4 = -\frac{1}{2}(x + 2)? (Select ALL that apply)
A. The line has a y-intercept of (0, 3).
B. The line passes through the point (2, -4).
C. The line has a slope of -\frac{1}{2}.
D. Any line with a slope of 2 would be perpendicular to this line.

SnapAndSolve AI · Accepted Answer

A. False. The y-intercept can be found by setting x = 0. The equation becomes y - 4 = -\frac{1}{2}(0 + 2), which simplifies to y - 4 = -1, so y = 3. Therefore, the y-intercept is (0, 3). B. False. Substitute x = 2 into the equation: y - 4 = -\frac{1}{2}(2 + 2) = -\frac{1}{2}(4) = -2. So, y - 4 = -2, which means y = 2. Therefore, the point (2, -4) is not on the line. C. True. The equation is in point-slope form y - 4 = -\frac{1}{2}(x + 2), which indicates the slope is -\frac{1}{2}. D. True. A line is perpendicular to another if the product of their slopes is -1. The slope of the given line is -\frac{1}{2}, so a line with a slope of 2 would be perpendicular because (-\frac{1}{2}) * 2 = -1.

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#2 Which of the following are true statements about the graph of y - 4 = -\frac{1}{2}(x + 2)?

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