Question

y=-2/3x +7y = 2x - 3For each equation, write the slope and y-intercept.Graph both equations on the same graph (do this on paper)

Answer 1

The given equations of the lines are in their slope-intercept form, that is:

`\begin{gathered} y=mx+b \\ \text{ Where m is the slope and} \\ b\text{ is the y-intercept of the line} \end{gathered}`

Then, we have:

• First equation

`\begin{gathered} y=-(2)/(3)x+7 \\ \boldsymbol{m=-(2)/(3)} \\ \boldsymbol{b=7} \end{gathered}`

• Second equation

`\begin{gathered} y=2x-3 \\ \boldsymbol{m=2} \\ \boldsymbol{b=-3} \end{gathered}`

Now, to graph the first equation, we can find two points through which the line passes:

• First point

If x = 3, then we have:

`\begin{gathered} y=-(2)/(3)x+7 \\ y=-(2)/(3)\cdot3+7 \\ y=-2+7 \\ y=5 \end{gathered}`

That means that the line passes through the point (3,5).

• Second point

If x = 6, then we have:

`\begin{gathered} y=-(2)/(3)x+7 \\ y=-(2)/(3)\cdot6+7 \\ y=-2\cdot2+7 \\ y=-4+7 \\ y=3 \end{gathered}`

That means that the line passes through the point (6,3).

To graph the second equation, we can find two points through which the line passes:

• First point

If x = 3, then we have:

`\begin{gathered} y=2x-3 \\ y=2\cdot3-3 \\ y=6-3 \\ y=3 \end{gathered}`

That means that the line passes through the point (3,3).

• Second point

If x = 4, then we have:

`\begin{gathered} y=2x-3 \\ y=2\cdot4-3 \\ y=8-3 \\ y=5 \end{gathered}`

That means that the line passes through the point (4,5).

Now that we know two points through which each line passes, we can graph them and then join them to obtain the graph of both equations: