Question

Graph the line with slope 1/3 passing through the point (4,2)

Answer 1

To graph a line we need two points, to find a second one we need the equation of the line. The equation of a line is given by:

`y-y_1=m(x-x_1)`

Plugging the values given we have:

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

Once we know the equation of a line we find a second point on the line, to do this we give a value to x and use the equation to find y. If x=1, then:

`\begin{gathered} y=(1)/(3)\cdot1+(2)/(3) \\ y=(1)/(3)+(2)/(3) \\ y=(3)/(3) \\ y=1 \end{gathered}`

Then we have the point (1,1).

Now that we have two points of the line we plot them on the plane and join them with a straight line. Therefore the graph of the line is: