Question

graph these equations:
$y = \frac{1}{5}x + 7$
$y = \frac{1}{5}x + 7$
click to select points on the graph.

Explanation:

Step1: Identify the slope-intercept form

The equation \( y = \frac{1}{5}x + 7 \) is in slope - intercept form \( y=mx + b \), where \( m=\frac{1}{5} \) (slope) and \( b = 7 \) (y - intercept).

Step2: Plot the y - intercept

The y - intercept \( b = 7 \) means the line crosses the y - axis at the point \( (0,7) \).

Step3: Use the slope to find another point

The slope \( m=\frac{1}{5}=\frac{\text{rise}}{\text{run}} \). From the point \( (0,7) \), we can rise 1 unit (up) and run 5 units (to the right) to get the point \( (0 + 5,7+1)=(5,8) \). We can also go in the opposite direction: rise - 1 unit (down) and run - 5 units (to the left) from \( (0,7) \) to get \( (0-5,7 - 1)=(-5,6) \).
Since both equations are the same (\( y=\frac{1}{5}x + 7 \) and \( y=\frac{1}{5}x + 7 \)), they represent the same line. So we can plot the points \( (0,7) \), \( (5,8) \), \( (-5,6) \) and draw a straight line through them.

(Note: Since the problem is about graphing, the final answer is the graph of the line \( y=\frac{1}{5}x + 7 \) with points like \( (0,7) \), \( (5,8) \), \( (-5,6) \) plotted and a line connecting them. But in text form, we can describe the process of graphing as above.)

Answer:

The graph is a straight line with y - intercept at \( (0,7) \), and other points such as \( (5,8) \) and \( (-5,6) \) (found using the slope \( \frac{1}{5} \)) plotted on it. The two given equations represent the same line, so the graph is of the line \( y=\frac{1}{5}x + 7 \).