Question

graph the line with the equation $y = \frac{1}{6}x + 3$.

Explanation:

Answer:

To graph \( y = \frac{1}{6}x + 3 \), follow these steps:

Step 1: Identify the y - intercept

The equation is in slope - intercept form \( y=mx + b \), where \( b \) is the y - intercept. For \( y=\frac{1}{6}x + 3 \), \( b = 3 \). So, the line crosses the y - axis at the point \( (0,3) \). Plot this point on the coordinate plane.

Step 2: Determine the slope

The slope \( m=\frac{1}{6} \). The slope is defined as \( m=\frac{\text{rise}}{\text{run}} \), which means for a run (change in \( x \)) of 6 units, the rise (change in \( y \)) is 1 unit.
Starting from the y - intercept \( (0,3) \), move 6 units to the right (since the run is positive, we move in the positive \( x \) - direction) and then 1 unit up (since the rise is positive, we move in the positive \( y \) - direction). This gives us the point \( (0 + 6,3+1)=(6,4) \). Plot this point.

Step 3: Draw the line

Use a straightedge to draw a line connecting the points \( (0,3) \) and \( (6,4) \). Extend the line in both directions to complete the graph of the line \( y=\frac{1}{6}x + 3 \).

(Note: You can also find another point by using a negative run and rise. For example, starting from \( (0,3) \), move 6 units to the left (run=- 6) and 1 unit down (rise = - 1) to get the point \( (0-6,3 - 1)=(-6,2) \), and then draw the line through \( (0,3) \) and \( (-6,2) \) as well, which should be the same line as the one through \( (0,3) \) and \( (6,4) \))