The slope of the line below is -5. Which of the following is the point-slope form of the line?A.y + 7 = 5(x - 2)B.y - 7 = -5(x + 2)C.y - 7 = 5(x + 2)D.y + 7 = -5(x - 2)
Question
The slope of the line below is -5. Which of the following is the point-slope form of the line?A.y + 7 = 5(x - 2)B.y - 7 = -5(x + 2)C.y - 7 = 5(x + 2)D.y + 7 = -5(x - 2)
Solution
The point-slope form of a line is given by the formula y - y1 = m(x - x1), where m is the slope of the line, and (x1, y1) is a point on the line.
Given that the slope of the line is -5, the equation of the line should have -5 multiplying the (x - x1) term.
Looking at the options:
A. y + 7 = 5(x - 2) - This equation has a slope of 5, not -5.
B. y - 7 = -5(x + 2) - This equation has a slope of -5, so it could be correct.
C. y - 7 = 5(x + 2) - This equation has a slope of 5, not -5.
D. y + 7 = -5(x - 2) - This equation has a slope of -5, but the y-coordinate of the point on the line should be -7, not 7.
So, the correct answer is B. y - 7 = -5(x + 2).
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