Question

Plot three points for the line and graph the line. Points (-4, 2)slope -1/3

Answer 1

We must plot three points for the line and graph it, for the line we know, a point and its slope, which are:

`\begin{gathered} (-4,2) \\ m=-(1)/(3) \end{gathered}`

To do this we first determine the function that describes this line, with the form y=mx+b where "y", we know it at a point being 2, "x" is -4 and m is the slope, now we clear b

`\begin{gathered} 2=-(1)/(3)\cdot(-4)+b \\ 2=(4)/(3)+b \\ b=2-(4)/(3) \\ b=(2)/(3) \end{gathered}`

So our function is as follows:

`y=-(1)/(3)x+(2)/(3)`

Having the function, we can now collect values for "x" and find the points to solve for and find the "y" value, in this case, we use x=-1, x=0, and x=2.

These values are random, they can be any desired value.

`\begin{gathered} x=-1 \\ y=-(1)/(3)\cdot(-1)+(2)/(3) \\ y=(1)/(3)+(2)/(3) \\ y=1 \end{gathered}`

The first point is (-1,1)

`\begin{gathered} x=0 \\ y=-(1)/(3)\cdot0+(2)/(3) \\ y=(2)/(3) \end{gathered}`

The second point is (0,2/3)

`\begin{gathered} x=2 \\ y=-(1)/(3)\cdot(2)+(2)/(3) \\ y=-(2)/(3)+(2)/(3) \\ y=0 \end{gathered}`

The third point is (2,0)

In conclusion the points are:

`\begin{gathered} (-1,1) \\ (0,(2)/(3)) \\ (2,0) \end{gathered}`

Now, to plot this line, what we have to do is plot the points found and draw a line through all the points.

The graph with the given point, the three points found and your graph should look like the following graph.