Given the Linear Equation:
[tex]5x+y=3x+2[/tex](a) You need to solve for "y", in order to rewrite it in Slope-Intercept Form, because that form is:
[tex]y=mx+b[/tex]Where "m" is the slope of the line and "b" is the y-intercept.
Then, you get:
[tex]\begin{gathered} y=-5x+3x+2 \\ y=-2x+2 \end{gathered}[/tex]Notice that:
[tex]\begin{gathered} m=-2 \\ b=2 \end{gathered}[/tex](b) You can graph the line by finding the x-intercept and the y-intercept. You already know that the y-intercept is:
[tex]b=2[/tex]Then, in order to find the x-intercept, you need to substitute this value of "y" into the equation and then solve for "x":
[tex]y=0[/tex]Because the value of "y" is zero when the line intersects the x-axis.
Therefore, you get:
[tex]\begin{gathered} y=-2x+2 \\ 0=-2x+2 \\ -2=-2x \\ \\ \frac{-2}{-2}=x \\ \\ x=1 \end{gathered}[/tex]Now you know that the line passes through these points:
[tex](1,0),(0,2)[/tex]Hence, you can graph it.
Therefore, the answers are:
(a) Equation in Slope-Intercept Form:
[tex]y=-2x+2[/tex](b) Graph:
