Question

use the line tool to graph the line passing through (3,2) whose slope is m = -\frac{1}{3}. provide your answer below:

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 $x_1 = 3$, $y_1=2$ and $m=-\frac{1}{3}$.

Step2: Plot the given point

Plot the point $(3,2)$ on the coordinate plane.

Step3: Use the slope to find another point

The slope $m =-\frac{1}{3}=\frac{\Delta y}{\Delta x}$. From the point $(3,2)$, if we move $\Delta x = 3$ units to the right (increase $x$ by 3), then $\Delta y=- 1$ (decrease $y$ by 1). So another point is $(3 + 3,2-1)=(6,1)$. We can also move $\Delta x=-3$ units to the left (decrease $x$ by 3) and $\Delta y = 1$ (increase $y$ by 1) to get the point $(3-3,2 + 1)=(0,3)$.

Step4: Draw the line

Use the line - tool to draw a straight line passing through the points $(3,2)$ and either $(6,1)$ or $(0,3)$.

Since this is a graphing task and we can't actually draw the line in this text - based format, the steps above describe how to graph the line. To graph it on the given grid:

1. Locate the point $(3,2)$ on the grid.
2. From $(3,2)$, move 3 units to the right and 1 unit down to get to the point $(6,1)$.
3. Connect the points $(3,2)$ and $(6,1)$ with a straight line using the line - tool on the given interface.

Answer:

Follow the steps above to graph the line on the provided grid using the line - tool.