Question

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

Explanation:

Step1: Identify the slope and y-intercept

The equation of the line is in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For the equation \(y=\frac{1}{5}x + 4\), the slope \(m=\frac{1}{5}\) and the y - intercept \(b = 4\).

Step2: Plot the y - intercept

The y - intercept is the point where the line crosses the y - axis. Since \(b = 4\), we plot the point \((0,4)\) on the coordinate plane.

Step3: Use the slope to find another point

The slope \(m=\frac{1}{5}\) can be thought of as \(\frac{\text{rise}}{\text{run}}\). The rise is \(1\) (upward) and the run is \(5\) (to the right). Starting from the point \((0,4)\), if we move up \(1\) unit and then move \(5\) units to the right, we get the point \((0 + 5,4+1)=(5,5)\). We can also use the negative slope values (down \(1\) and left \(5\)) to get another point, for example, starting from \((0,4)\), moving down \(1\) and left \(5\) gives \((0 - 5,4-1)=(-5,3)\).

Step4: Draw the line

Using a straightedge, draw a line that passes through the points we have plotted (such as \((0,4)\), \((5,5)\), and \((-5,3)\)). This line represents the graph of the equation \(y=\frac{1}{5}x + 4\).

(Note: Since the problem is about graphing, the main steps are identifying the key features of the line (slope and y - intercept) and then plotting points to draw the line. If we were to describe the graph, the line has a positive slope (since the coefficient of \(x\) is positive), a y - intercept at \((0,4)\), and passes through other points calculated using the slope.)

Answer:

To graph \(y=\frac{1}{5}x + 4\):

1. Plot the y - intercept \((0,4)\).
2. Use the slope \(\frac{1}{5}\) (rise = 1, run = 5) to find additional points (e.g., \((5,5)\), \((-5,3)\)).
3. Draw a straight line through these points. The line has a positive slope, crosses the y - axis at \((0,4)\), and extends infinitely in both directions.