Final answer:
The equation of the line passing through the points (7, -3) and (8, -7) is found by first calculating the slope (m = -4), then using the point-slope form with one of the points to establish y = -4x + 25 as the final equation in slope-intercept form.
Step-by-step explanation:
To write an equation of the line passing through the points (7, -3) and (8, -7), we first find the slope (m) of the line. The slope is obtained by the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the points the line passes through. Substituting the given points into the formula, we get:
m = (-7 - (-3)) / (8 - 7) = -4 / 1 = -4
Now that we have the slope, we use the point-slope form of the equation of a line, which is y - y1 = m(x - x1). We can take either of the given points for (x1, y1). Using (7, -3), we substitute into the formula:
y - (-3) = -4(x - 7)
To find the y-intercept (b), we simplify the equation to the slope-intercept form, y = mx + b:
y + 3 = -4x + 28
y = -4x + 25
Thus, the equation of the line passing through the points (7, -3) and (8, -7) is y = -4x + 25.