Answer :
To write the equation of a line in slope-intercept form you need to find slope (m) and y-intercept (b)
Slope:
Two parallel lines have the same slope.
An equation parallel to:
[tex]6x-5y=20[/tex]has the same slope.
To identify the slope write the equation in form y=m+b (solve y):
[tex]\begin{gathered} -5y=-6x+20 \\ y=\frac{-6}{-5}x+\frac{20}{-5} \\ \\ y=\frac{6}{5}x-4 \end{gathered}[/tex]Slope: m= 6/5Y-intercept:
To find the y-intercept use the given point (5,3) and the slope in the next equation:
[tex]y=mx+b[/tex]y=3
x=5
m=6/5
Find b:
[tex]\begin{gathered} 3=\frac{6}{5}(5)+b \\ \\ 3=\frac{30}{5}+b \\ \\ 3=6+b \\ 3-6=b \\ -3=b \end{gathered}[/tex]y-intercept: b= -3Equation:[tex]y=\frac{6}{5}x-3[/tex]