Question

Find the equation of the line passing through the points (−16,5) and (32,−37) Write your answer in the form y=mx+b Answer y= Write your answers as integers or as reduced fractions in the form A/B.

Answer 1

The equation of the line passing through the points (−16,5) and (32,−37) is y = -7/8x - 2.

Step-by-step explanation:

Finding the Equation of a Line

To find the equation of the line passing through two points, we need to determine the slope (m) and the y-intercept (b). The general form of the equation of a line is y = mx + b, where m represents the slope, and b represents the y-intercept.

First, let's find the slope using the points (−16,5) and (32,−37). The slope is the rise over the run, defined as the change in y over the change in x. Therefore:

m = (y2 - y1) / (x2 - x1) = (−37 - 5) / (32 - (−16)) = (−42) / (48) = −7/8

Next, we can substitute one of the points into the equation along with our found slope to calculate the y-intercept:

5 = (−7/8)(−16) + b => b = 5 - (7/2)

After simplifying, we find that b = −2.

Thus, the equation of the line is:

y = −7/8x − 2.