Question

question 6, 2.3.27 graph the line that contains the point (2,2) and has a slope of $\frac{1}{3}$. use the graphing tool to graph the line. click to enlarge graph

Explanation:

Step1: Recall point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope. Here, $x_1 = 2,y_1 = 2,m=\frac{1}{3}$. So the equation is $y - 2=\frac{1}{3}(x - 2)$.

Step2: Expand the equation

$y-2=\frac{1}{3}x-\frac{2}{3}$. Then $y=\frac{1}{3}x-\frac{2}{3}+2=\frac{1}{3}x+\frac{4}{3}$.

Step3: Find another point

Let $x = 5$, then $y=\frac{1}{3}\times5+\frac{4}{3}=\frac{5 + 4}{3}=3$. So another point on the line is $(5,3)$.

Step4: Graph the line

Plot the points $(2,2)$ and $(5,3)$ on the coordinate - plane and draw a straight line passing through them.

Answer:

Graph the line passing through the points $(2,2)$ and $(5,3)$ on the given grid.