Question

Follow the steps below to write the point-slope form of the given line that passes through the points (0,-3) and (4,1). a. using variables, write out the formula for the point-slope form of the equation. b. determine the slope of the line. c. identify (0, -3) as (x1, y1). d. write the point-slope form of the line that passes through the points (0, -3) and (4, 1). show all work on how you found the slope. use the box provided to submit all of your calculations and final answers. simplify the answer as needed.

Answer 1

To write the point-slope form of a line, you use the formula y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. The slope of the line passing through the points (0, -3) and (4, 1) is 1. The point (0, -3) is identified as (x1, y1) and the point-slope form of the line becomes y + 3 = x.

Step-by-step explanation:

a. The point-slope form of the equation is given by y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line.

b. To find the slope, we use the formula m = (y2 - y1) / (x2 - x1). Using the points (0, -3) and (4, 1), we have m = (1 - (-3)) / (4 - 0) = 4 / 4 = 1.

c. The point (0, -3) has coordinates (x1, y1).

d. Substituting the values m = 1, x1 = 0, and y1 = -3 into the point-slope form, we get y - (-3) = 1(x - 0) simplifying further we find y + 3 = x.