Question

Graph 5x + y = 3x + 2(a) Rewrite the equation in slope intercept form. Show your work.(b) Graph the line. If you aren't able to draw on the graph using the technology you have available,then just describe it in words - tell where it is located

Answer 1

Given the Linear Equation:

`5x+y=3x+2`

(a) You need to solve for "y", in order to rewrite it in Slope-Intercept Form, because that form is:

`y=mx+b`

Where "m" is the slope of the line and "b" is the y-intercept.

Then, you get:

`\begin{gathered} y=-5x+3x+2 \\ y=-2x+2 \end{gathered}`

Notice that:

`\begin{gathered} m=-2 \\ b=2 \end{gathered}`

(b) You can graph the line by finding the x-intercept and the y-intercept. You already know that the y-intercept is:

`b=2`

Then, in order to find the x-intercept, you need to substitute this value of "y" into the equation and then solve for "x":

`y=0`

Because the value of "y" is zero when the line intersects the x-axis.

Therefore, you get:

`\begin{gathered} y=-2x+2 \\ 0=-2x+2 \\ -2=-2x \\ \\ (-2)/(-2)=x \\ \\ x=1 \end{gathered}`

Now you know that the line passes through these points:

`(1,0),(0,2)`

Hence, you can graph it.

Therefore, the answers are:

(a) Equation in Slope-Intercept Form:

`y=-2x+2`

(b) Graph: