Final answer:
The equation of the line that passes through (7, -7) and (3, 8) is found by first calculating the slope (m) which is -15/4, and then using the point-slope form to arrive at the line's equation, which is y = (-15/4)x + 77/4.
Step-by-step explanation:
To write the equation of the line that passes through the points (7, -7) and (3, 8), you first need to find the slope (m) of the line. The slope is calculated by the change in y divided by the change in x:
m = (y2 - y1) / (x2 - x1)
Substitute the points into the formula:
m = (8 - (-7)) / (3 - 7)
m = 15 / -4
So the slope m is -15/4.
Now use point-slope form to write the equation of the line:
y - y1 = m(x - x1)
Using point (7, -7):
y - (-7) = (-15/4)(x - 7)
Simplify the equation:
y + 7 = (-15/4)x + (15/4)*7
y = (-15/4)x + 105/4 - 28/4
y = (-15/4)x + 77/4
Therefore, the equation of the line is y = (-15/4)x + 77/4.