Final answer:
To find the slope-intercept form of the line through (-2, -3) and (4, -15), we calculate the slope as -2 and use it with one of the points to find the y-intercept as -7, resulting in the equation y = -2x - 7.
Step-by-step explanation:
To find the slope-intercept form of the equation of the line passing through the points (-2, -3) and (4, -15), we first need to calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1).
Substituting in the given points gives us:
m = (-15 - (-3)) / (4 - (-2)) = (-12) / (6) = -2.
Now that we have the slope, we can use one of the points to find the y-intercept (b). The slope-intercept form is y = mx + b, so let’s use the point (-2, -3):
-3 = (-2)(-2) + b
-3 = 4 + b
b = -3 - 4
b = -7
Therefore, the slope-intercept form of the equation is:
y = -2x - 7.