Final answer:
The equation of the line that passes through the points (-6, 13) and (3, 1) is (4/3)x + y = 5.
Step-by-step explanation:
To find the equation of the line that passes through the points (-6, 13) and (3, 1), we can use the point-slope form. The point-slope form of a linear equation is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. First, we need to find the slope:
m = (y2 - y1) / (x2 - x1)
Plugging in the coordinates, we get:
m = (1 - 13) / (3 - (-6))
m = -12/9
Simplifying, we get:
m = -4/3
Now that we have the slope, we can choose one of the points and the slope to write the equation:
y - y1 = m(x - x1)
Using the point (-6, 13):
y - 13 = (-4/3)(x - (-6))
Simplifying, we get:
y - 13 = (-4/3)(x + 6)
Expanding, we get:
y - 13 = (-4/3)x - 8
Finally, rearranging the equation to the standard form, we get:
(4/3)x + y = 5