Question

Write the point-slope form of the equation of the line that passes through the points (6, -9) and (7, 1). Include your work in your final answer.

A. y - (-9) = m(x - 6)
B. y + 9 = m(x + 6)
C. y - 1 = m(x - 7)
D. y - 1 = m(x - 6)

Answer 1

The point-slope form of the equation of the line through the points (6, -9) and (7, 1) is y + 9 = 10(x - 6), and the correct point-slope form equation from the options given is A. y - (-9) = m(x - 6).

Step-by-step explanation:

The student has asked for the point-slope form of the equation of the line that passes through the points (6, -9) and (7, 1). To write this equation, we first calculate the slope (m) using the formula m=(y2-y1)/(x2-x1). Using the given points, the slope is m=(1-(-9))/(7-6)=10. Next, we use one of the points and the slope to write the equation in point-slope form. Option A is the correct answer, since it uses the point (6, -9) and incorporates the negative y-coordinate properly: y - (-9) = m(x - 6).