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:

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

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:

$\begin{gathered} y=\frac{1}{3}\cdot1+\frac{2}{3} \\ y=\frac{1}{3}+\frac{2}{3} \\ y=\frac{3}{3} \\ y=1 \end{gathered}$

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: