Answer:
y = -5x + 31
Explanation:
To find the equation of a line parallel to the line 5x + y = 5, we first need to rearrange it in slope-intercept form, which is
y = -5x + 5. (We see that the slope of this line is -5)
A line parallel to this line will have the same slope of -5. Now, we need to find the equation of a line that passes through the point (8,-9) with slope -5.
We can use the point-slope form of the line to find the equation. The point-slope form of a line is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.
Substituting the values we have, we get:
y - (-9) = -5(x - 8)
Simplifying this equation, we get:
y + 9 = -5x + 40
y = -5x + 31
Therefore, the equation of the line parallel to 5x + y = 5 that passes through the point (8, -9) is y = -5x + 31.