Question

graph the following linear equation on the grid. the equation y = x has been graphed for you.
( y = \frac{6}{6}x + 7 )

Explanation:

Step1: Simplify the slope

The equation is \( y = \frac{6}{6}x + 7 \). Simplify \( \frac{6}{6} \) to \( 1 \), so the equation becomes \( y = x + 7 \).

Step2: Identify slope and y - intercept

For a linear equation in the form \( y = mx + b \), \( m \) is the slope and \( b \) is the y - intercept. Here, \( m = 1 \) (same slope as \( y=x \)) and \( b = 7 \). So the line is parallel to \( y = x \) but shifted up 7 units. To graph it, start at the y - intercept \( (0,7) \) and use the slope (rise 1, run 1) to plot other points.

(Note: Since the question is about graphing, the main steps are understanding the equation's form and using slope - intercept to graph. If we were to describe the graphing process in steps for plotting:

1. Locate the y - intercept: Find the point where \( x = 0 \). Substituting \( x = 0 \) into \( y=x + 7 \), we get \( y=7 \), so the point is \( (0,7) \).
2. Use the slope: The slope \( m = 1=\frac{1}{1} \). From the point \( (0,7) \), move 1 unit up (rise) and 1 unit to the right (run) to get the next point \( (1,8) \). We can also move 1 unit down and 1 unit to the left from \( (0,7) \) to get \( (- 1,6) \). Then draw a straight line through these points.)

Answer:

To graph \( y=\frac{6}{6}x + 7\) (which simplifies to \( y=x + 7\)):

1. Plot the y - intercept at \( (0,7) \).
2. Use the slope \( m = 1\) (rise 1, run 1) to plot additional points (e.g., \( (1,8) \), \( (-1,6) \)) and draw a straight line through them (parallel to \( y = x\) but shifted up 7 units).