Answer: First, remember that parallel lines have the same slope. So we first need to find the slope of the line we are given, 3x+2y=27. The quickest way to find the slope of this line is to put it into slope-intercept form (y=mx+b)
subract 3x from both sides:
2y=-3x+27
divide each term by 2:
y=-3/2x +27/2
Now we can see that the slope is -3/2.
From here, we use the slope we found and the ordered pair given (7,-4) and find the equation of the new line. We will have to use point-slope form (y-y1)=m(x-X1) to find the new line because the ordered pair given is not the y-intercept.
(y-(-4))=-3/2(x-7)
distribute -3/2:
(y-(-4))= -3/2x + 21/2
simplify double negative on left side of equals sign:
y+4=-3/2x + 21/2
Subtract 4 from both sides:
y= -3/2x + 13/2
This is your answer in slope intercept form. Because the directions specifically ask for standard form, we have one more step. Standard form (ax+by=c) needs the terms with x and y to be on the same side of the equals sign. So, we simply have to move the term with x (-3/2x) to the other side by adding.
Finished product:
3/2x+y= 13/2
Step-by-step explanation:
