Question

What is an equation in POINT-SLOPE FORM of the line that passes through (-5, 3) and (10, 13)?

a) y - 3 = 2(x + 5)
b) y - 3 = 2(x - 5)
c) y - 13 = 2(x - 10)
d) y - 13 = 2(x + 10)

Answer 1

The equation in point-slope form for the line passing through (-5, 3) and (10, 13) is y - 3 = (2/3)(x + 5).

Step-by-step explanation:

The student is asking to find the equation in point-slope form of the line that passes through the points (-5, 3) and (10, 13). To determine the correct equation, we first need to calculate the slope of the line. The slope (m) is given by the change in y over the change in x, that is, m = (y2 - y1) / (x2 - x1). Using the points given, we plug in the values to get m = (13 - 3) / (10 - (-5)) = 10 / 15 = 2/3. Now we use the point-slope form equation y - y1 = m(x - x1), choosing one of the points to substitute, let's use the first point (-5, 3), thus the equation becomes y - 3 = (2/3)(x + 5). This equation represents the line in point-slope form.