Question 174012
first you must write the equation in y=mx+b format or slope intercept form.  the slope is m and the y intercept is b. Since the equation is already in that form we know what the slope is y={{{5}}}x-3. m=5.  therefore as you say a line parallel to that line must have this same slope.
:
so we have the slope of 5. In order to write an equation of a line we need the slope and a point. We have both as (4,7) is the given point. Now we use the point slope formula which is y-k=m(x-h) where (h,k) is any point on the line
:
y-7=5(x-4)
:
y-7=5x-20
:
{{{highlight(5x-y=13)}}} standard form {{{highlight(y=5x-13)}}} point slope form