First, we need to solve the equation 4x+5y=7 to make it slope intercept form and find the slope of the line, because parallel lines have the same slope.
4x+5y=7
Subtract 4x from both sides.
5y=-4x+7
Divide both sides by 5.
y=-4/5x+7/5
The slope of the line is -4/5x. Plug that in to the blank slope intercept form equation, y=mx+b, with m being the slope and b being the y-intercept.
y=-4/5x+b
Now, we need to solve for the y-intercept. We can do this by plugging in the given coordinates (4,-3) into the above equation for x and y respectively:
-3=-4/5(4)+b
-3=-16/5+b
Add -16/5 to both sides.
1/5=b
The y-intercept is 1/5, plug this into the equation:
[tex]y=-\frac{4}{5}x+\frac{1}{5}[/tex]
Your equation is the above equation.
I hope this helps :)
