Question

What is the equation in point-slope form of a line that passes through the points (5, −3) and (−2, 9) ? A. y−3=−2(x + 5)

B. y + 3=−127(x−5)
C. y + 3=−2(x−5)
D. y−3=−127(x + 5)

Answer 1

The equation of the line in point-slope form that passes through the points (5, -3) and (-2, 9) is y + 3 = -12/7(x - 5), which corresponds to option B.

Step-by-step explanation:

Finding the Equation of a Line in Point-Slope Form

The question asks for the equation in point-slope form of a line that passes through the points (5, -3) and (-2, 9). To find this, we first calculate the slope (m) of the line using the formula m = (y2 - y1) / (x2 - x1). Plugging in our points, we get m = (9 - (-3)) / (-2 - 5) = 12 / -7 = -12/7.

Now, we need to write the equation in point-slope form, which is y - y1 = m(x - x1), where (x1, y1) is one of the given points. Using the point (5, -3) and our calculated slope, the equation is y + 3 = -12/7(x - 5). This matches option B. Therefore, the equation of the line in point-slope form is:

y + 3 = -12/7(x - 5)