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=-(2)/(3) \\ (x_p,y_p)=(1,-3) \end{gathered}`
`\begin{gathered} y-(-3)=-(2)/(3)(x-1) \\ y+3=-(2)/(3)x+(2)/(3) \\ y=-(2)/(3)x+(2)/(3)-3 \\ y=-(2)/(3)x+(2-9)/(3) \\ y=-(2)/(3)x-(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=-(2)/(3)\cdot0-(7)/(3) \\ y=-(7)/(3) \end{gathered}`

And x = 2:

`\begin{gathered} y=-(2)/(3)\cdot2-(7)/(3) \\ y=(-4-7)/(3) \\ y=(-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: