Question

What is the equation in point-slope form of the line passing through (-2, 1) and (4, 13)?

A. (y - 1 = -2(x - 4))
B. (y - 1 = 2(x + 2))
C. (y - 13 = -2(x + 2))
D. (y - 13 = 2(x + 4))

Answer 1

The equation of the line passing through (-2, 1) and (4, 13) in point-slope form is B. y - 1 = 2(x + 2), after calculating the slope as 2.

Step-by-step explanation:

To find the equation of the line passing through the points (-2, 1) and (4, 13), we first calculate the slope (m). The slope is given by the change in y over the change in x (m = (y2 - y1) / (x2 - x1)).

Slope, m = (13 - 1) / (4 - (-2)) = 12 / 6 = 2.

Now, we can use the point-slope form which is y - y1 = m(x - x1), where (x1, y1) is a point on the line. Using the point (-2, 1) and the slope 2, the point-slope form is y - 1 = 2(x - (-2)), which simplifies to:

Equation B. y - 1 = 2(x + 2).