Question

What is the equation of a line that has y-intercept of -3 and is parallel to the line 3x=4+5y

Answer 1

The equation of a line with slope m and y-intercept b in slope-intercept form is:

`y=mx+b`

On the other hand, two lines are parallel if they have the same slope.

First, find the slope of the given line by isolating y from the equation.

Next, write down the equation of a line with y-intercept -3 and with the same slope as the given line to find the equation of a line that satisfies the described characteristics.

The equation of the given line is 3x=4+5y. Isolate y:

`\begin{gathered} 3x=4+5y \\ \Rightarrow3x-4=5y \\ \Rightarrow(3x-4)/(5)=y \\ \Rightarrow(3)/(5)x-(4)/(5)=y \\ \therefore y=(3)/(5)x-(4)/(5) \end{gathered}`

Since the coefficient of x is 3/5, then, the value of the slope of the given line is 3/5.

Replace m=3/5 and b=-3 into the general equation of a line in slope-intercept form to find the equation of a line that has y-intercept of -3 and is parall