Question

Graph a line with slope 2/3 passing through the point (1,1)

Answer 1

The general equation of a line is:

`y=mx+b`

Where m is the slope and b the y-intercept.

Given the slope and one point, you can replace these values to find the y-intercept b:

`\begin{gathered} 1=(2)/(3)\cdot1+b \\ 1=(2)/(3)+b \\ 1-(2)/(3)=b \\ b=(1\cdot3-1\cdot2)/(1\cdot3)=(3-2)/(3) \\ b=(1)/(3) \end{gathered}`

Then, the equation of the line is:

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

To graph the line, you can make a table of values first:

x y

-1 -1/3

0 1/3

1 1

2 5/3

And the graph will look like: