Answer: To find an equation of the line that passes through the point (8, -7) and is parallel to the line x + 2y = 18, we first need to find the slope of the line x + 2y = 18.
We can rewrite the equation x + 2y = 18 as 2y = -x + 18 and then solve for y to get:
y = (-1/2)x + 9
This is in slope-intercept form, y = mx + b, where the slope, m, is -1/2.
Since the line we want to find is parallel to this line, it will have the same slope, which is -1/2. We can use the point-slope form of a linear equation to find the equation of the line that passes through (8, -7) with slope -1/2:
y - (-7) = (-1/2)(x - 8)
Simplifying the right side of the equation gives:
y + 7 = (-1/2)x + 4
Subtracting 7 from both sides gives:
y = (-1/2)x - 3
So the equation of the line that passes through (8, -7) and is parallel to x + 2y = 18 is y = (-1/2)x - 3.
Explanation: