Question

A line passes through the points (3, 7) and (6, 13). What is an equation of a line in point-slope form? Select all that apply.

A) y - 7 = 2(x - 3)
B) y - 13 = 2(x - 6)
C) y - 7 = (x - 3)
D) y - 13 = (x - 6)
E) y - 7 = -2(x - 3)
F) y - 13 = -2(x - 6)

Answer 1

The equation of a line in point-slope form, given two points (3, 7) and (6, 13), can be derived by finding the slope and applying it to either point. The correct equations are y - 7 = 2(x - 3) and y - 13 = 2(x - 6), which correspond to options A and B respectively.

Step-by-step explanation:

The first step to finding the equation of a line in point-slope form is to determine the slope of the line that passes through two given points, (3, 7) and (6, 13). The slope (m) is found by dividing the change in y by the change in x:

m = (y2 - y1) / (x2 - x1) = (13 - 7) / (6 - 3) = 6 / 3 = 2

Now, using the slope and one of the points, we can write the equation using the point-slope formula, y - y1 = m(x - x1). Using the point (3, 7), the equation is:

y - 7 = 2(x - 3), which matches option A.

Similarly, using the point (6, 13), the equation is:

y - 13 = 2(x - 6), which matches option B.

Therefore, the lines in the point-slope form that passes through the points (3, 7) and (6, 13) are given by options A and B.