Final answer:
The equation of the line that goes through the points (9,-9) and (13,-1) is y = 2x - 27, where the slope (m) is 2 and the y-intercept (b) is -27.
Step-by-step explanation:
The question involves finding the equation of a line that passes through the points (9,-9) and (13,-1). To find the equation, we need to determine the slope (m) and the y-intercept (b) of the line. The slope can be found using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the given points.
First, calculate the slope:
m = (-1 - (-9)) / (13 - 9)
m = (8) / (4)
m = 2
Now with the slope, use point-slope form to create the equation, which is y - y1 = m(x - x1). Selecting point (9, -9):
y - (-9) = 2(x - 9)
y + 9 = 2x - 18
y = 2x - 27
This is the equation of the line in slope-intercept form, which is y = mx + b.