Question

Graph the line through the point (1, -3) having a slope of -2/3 then give two other points on the line

Answer 1

To graph this line, we can start by finding its equation.

Since we have the slope and a point in the line, we can use the slope-point form:

$y-y_p=m(x-x_p)$$\begin{gathered} m=-\frac{2}{3} \\ (x_p,y_p)=(1,-3) \end{gathered}$$\begin{gathered} y-(-3)=-\frac{2}{3}(x-1) \\ y+3=-\frac{2}{3}x+\frac{2}{3} \\ y=-\frac{2}{3}x+\frac{2}{3}-3 \\ y=-\frac{2}{3}x+\frac{2-9}{3} \\ y=-\frac{2}{3}x-\frac{7}{3} \end{gathered}$

Using this, we can get the two other points the question wants before graphing the line.

We can, for example, pick x = 0:

$\begin{gathered} y=-\frac{2}{3}\cdot0-\frac{7}{3} \\ y=-\frac{7}{3} \end{gathered}$

And x = 2:

$\begin{gathered} y=-\frac{2}{3}\cdot2-\frac{7}{3} \\ y=\frac{-4-7}{3} \\ y=\frac{-11}{3} \end{gathered}$

So, we have the points (0, -7/3) and (2, -11/3).

To graph, we can plot these points and than connect them, like this: