Final answer:
The equation of the line passing through the points (-3, 7) and (5, -9) is y = -2x + 1, calculated by determining the slope between the points and then using one of the points to find the y-intercept.
Step-by-step explanation:
To find the equation of the line passing through the points (-3, 7) and (5, -9), we first need to calculate the slope of the line. The slope (m) is found by the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points through which the line passes. Plugging in our values, we get:
m = (-9 - 7) / (5 - (-3)) = -16 / 8 = -2
Now that we have the slope, we can use one of the points and the slope to write the equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. Let's use the point (-3, 7) and the slope -2 to find b.
7 = (-2)(-3) + b
b = 7 - 6
b = 1
The equation of the line in slope-intercept form is y = -2x + 1.