Answer:
y=1/3x+7
Step-by-step explanation:
Hi there!
We're given the equation x-3y=21 and we want to find the equation of the line parallel to x-3y=21 that passes through (-6,5)
Parallel lines have the same slopes, but different y intercepts
So we need to find the slope of x-3y=21
To do that, we can convert x-3y=21 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).
We'll need to isolate y onto one side
subtract x from both sides
-3y=-x+21
divide both sides by -3
y=1/3x-7
1/3 is in the place where m is, so 1/3 is the slope of the line
it's also the slope of the line parallel to x-3y=21
here's the equation of the line parallel to x-3y=21 so far:
y=1/3x+b
we need to find b
as the line passes through (-6,5), we can use it to solve for b
substitute -6 as x and 5 as y
5=1/3(-6)+b
multiply
5=-2+b
add 2 to both sides
7=b
Substitute 7 as b into the equation
y=1/3x+7
Hope this helps!
