How do I write an equation that passes through the given line and is parallel to the line: (4, 7), y=5x-3

With lines of the form y=mx+b lines are parallel as long as m is the same->m=5

so we know the new line also has the form y=5x+b, so now we have to calculate the b to pass through (4,7)

for this insert x=4, and y=7 to solve for b

7=5*4+b

7=20+b

-13=b

so the parallel line through (4,7) has the equation y=5x-13