Question

graph the line with the equation $y = \frac{1}{6}x + 5$.

Explanation:

Step1: Identify the slope and y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For \(y=\frac{1}{6}x + 5\), the y - intercept \(b = 5\) and the slope \(m=\frac{1}{6}\).

Step2: Plot the y - intercept

The y - intercept is the point where \(x = 0\). So we plot the point \((0,5)\) on the y - axis.

Step3: Use the slope to find another point

The slope \(\frac{1}{6}\) means "rise over run", or \(\frac{\text{change in }y}{\text{change in }x}\). So from the point \((0,5)\), we move up 1 unit (change in \(y = 1\)) and then move to the right 6 units (change in \(x=6\)). This gives us the point \((0 + 6,5+1)=(6,6)\).

Step4: Draw the line

Draw a straight line through the points \((0,5)\) and \((6,6)\) (we can also find more points by using the slope in the other direction, like moving down 1 and left 6 from \((0,5)\) to get \((- 6,4)\) and draw the line through these points as well).

Answer:

To graph \(y=\frac{1}{6}x + 5\), plot \((0,5)\) (y - intercept), then use the slope \(\frac{1}{6}\) to find another point (e.g., \((6,6)\)) and draw a line through these points.