Question

write the equation of the line in slope-intercept from through point(5,3) and is parallel to 6x-5y=20

Answer 1

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:

`6x-5y=20`

has the same slope.

To identify the slope write the equation in form y=m+b (solve y):

`\begin{gathered} -5y=-6x+20 \\ y=(-6)/(-5)x+(20)/(-5) \\ \\ y=(6)/(5)x-4 \end{gathered}`Slope: m= 6/5

Y-intercept:

To find the y-intercept use the given point (5,3) and the slope in the next equation:

`y=mx+b`

y=3

x=5

m=6/5

Find b:

`\begin{gathered} 3=(6)/(5)(5)+b \\ \\ 3=(30)/(5)+b \\ \\ 3=6+b \\ 3-6=b \\ -3=b \end{gathered}`y-intercept: b= -3Equation:
`y=(6)/(5)x-3`