Question

graph the equation using the point and the slope
$y - 1 = \frac{1}{3}(x - 2)$
use the graphing tool to graph the equation. use the point contained in the equation when drawing the line.
click to enlarge graph

Explanation:

Step1: Identify the form of the equation

The given equation is \( y - 1=\frac{1}{3}(x - 2) \), which is in the point - slope form \( y - y_1=m(x - x_1) \), where \( (x_1,y_1)=(2,1) \) and the slope \( m = \frac{1}{3} \).

Step2: Plot the point

First, we plot the point \( (2,1) \) on the coordinate plane.

Step3: Use the slope to find another point

The slope \( m=\frac{1}{3}=\frac{\text{rise}}{\text{run}} \). Starting from the point \( (2,1) \), we move up 1 unit (because the rise is 1) and then move to the right 3 units (because the run is 3). This gives us the point \( (2 + 3,1+1)=(5,2) \). We can also move down 1 unit and to the left 3 units from \( (2,1) \) to get the point \( (2-3,1 - 1)=(-1,0) \).

Step4: Draw the line

After plotting the point \( (2,1) \) and using the slope to find at least one more point (like \( (5,2) \) or \( (-1,0) \)), we draw a straight line passing through these points.

(Note: Since this is a graphing problem, the final answer is the graph of the line passing through the point \( (2,1) \) with a slope of \( \frac{1}{3} \). If we were to describe the key points: the line passes through \( (2,1) \), \( (5,2) \), \( (-1,0) \) etc. and has a positive slope of \( \frac{1}{3} \))

Answer:

The graph of the equation \( y - 1=\frac{1}{3}(x - 2) \) is a straight line passing through the point \( (2,1) \) with a slope of \( \frac{1}{3} \). To graph it, plot \( (2,1) \), then use the slope \( \frac{1}{3} \) (rise 1, run 3) to find additional points (e.g., \( (5,2) \), \( (-1,0) \)) and draw a line through them.