Question

graph the line with the equation $y = \frac{1}{5}x + 4$.

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 \(y=\frac{1}{5}x + 4\), the slope \(m=\frac{1}{5}\) and the y - intercept \(b = 4\). So, the line crosses the y - axis at \((0,4)\).

Step2: Use the slope to find another point

The slope \(\frac{1}{5}\) means "rise over run", or \(\frac{\text{change in }y}{\text{change in }x}\). From the y - intercept \((0,4)\), we can go up 1 unit (change in \(y = 1\)) and then to the right 5 units (change in \(x=5\)) to get the point \((0 + 5,4+1)=(5,5)\). We can also go down 1 unit and to the left 5 units from \((0,4)\) to get \((0 - 5,4 - 1)=(-5,3)\).

Step3: Plot the points and draw the line

Plot the points \((0,4)\), \((5,5)\) (and/or \((-5,3)\)) on the coordinate plane. Then, draw a straight line through these points.

Answer:

To graph \(y=\frac{1}{5}x + 4\), plot the y - intercept \((0,4)\), then use the slope \(\frac{1}{5}\) to find another point (e.g., \((5,5)\) or \((-5,3)\)) and draw a line through the plotted points.