Answer:
y = (3/5)x+3.6
Explanation:
Let's look for an equation of the standard form: y=mx+b, where m is the slope and b is the y-intercept (the value of y when x is 0). Parallel lines have the same slope, m. Next, rearrange the reference line to standard format:
3x-5y=10
-5y = -3x + 10
y = (3/5)x + 2
Now we can easily find the slope. The slope of the reference line is (3/5). That will also be the slope of the parallel line, so we can write:
y = (3/5)x + b
We need a value of b that will shift the line so that it touches point (-1,3) . ["passes through"]. Enter that point into the above equation and solve for b:
y = (3/5)x + b
(3) = (3/5)*(-1) + b for point (-1,3)
3 = -(3/5) + b
-(3/5) = 3-b
-b = -3 - (3/5)
b = 3+(3/5)
b = (18/5), or 3.6
The equation becomes y = (3/5)x+3.6
See the attached graph.
[Parallel lines have a lot in common. Too bad they'll never meet.]