Answer:
y=-1/2x-4
Explanation:
Hi there!
We're given the equation x+2y=14 and we want to find a line that is parallel to it and passes through (-8,0)
Parallel lines have the same slopes, but different y intercepts.
So let's find the slope of x+2y=14
we do this by converting x+2y=14 from standard form (ax+by=c where a, b, and c are integers) to slope-intercept form (y=mx+b, where m is the slope and b is the y intercept).
for x+2y=14, to convert to slope-intercept form, start by subtracting x from both sides
2y=-x+14
divide both sides by 2
y=-1/2x+7
so the slope of x+2y=14 is -1/2
The slope of the new line (the one parallel to x+2y=14 and passes through (-8,0) will also have a slope of -1/2).
Here's the equation of that line so far:
y=-1/2x+b
we need to find b (y intercept)
as the equation will pass through (-8,0), we can use it to solve for b
substitute -8 as x and 0 as y
0=-1/2(-8)+b
multiply
0=4+b
subtract 4 from both sides
-4=b
substitute into the equation
y=-1/2x-4
Hope this helps! :)