Final answer:
The equation in slope-intercept form for the given line is y = (-8/7)x + 4.
Step-by-step explanation:
To find the equation in slope-intercept form, we will use the formula y = mx + b, where m is the slope and b is the y-intercept. First, we need to find the slope (m) using the formula m = (y2 - y1) / (x2 - x1). From the given points (7,-4) and (14,-12), the slope is calculated as m = (-12 - (-4)) / (14 - 7) = -8/7. Next, we can use the slope and any of the given points to find the y-intercept (b) by substituting the values into the equation. Let's use the point (7,-4):
-4 = (-8/7)(7) + b
Solving the equation, we get b = -4 + 8 = 4. So the equation of the line is y = (-8/7)x + 4.
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