Explanation:
To find the equation of a line parallel to a given line, we need to use the fact that parallel lines have the same slope. Therefore, we can find the slope of the given line and use it to find the equation of the parallel line that passes through the given point.
Let's start by rearranging the given line -2x+y=9 into slope-intercept form, y=mx+b, where m is the slope and b is the y-intercept:
-2x+y=9
y=2x+9
So, the slope of the given line is 2.
Now, we can use the point-slope form of the equation of a line to find the equation of the parallel line that passes through the point (-4,8):
y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope of the parallel line.
Plugging in the values, we get:
y - 8 = 2(x + 4)
Simplifying, we get:
y - 8 = 2x + 8
y = 2x + 16
Therefore, the equation of the line parallel to -2x+y=9 that passes through the point (-4,8) is y = 2x + 16.