Question

graph this line using the slope and y-intercept:
$y = \frac{1}{4}x$
click to select points on the graph.
(graph with x-axis from -10 to 10 and y-axis from -6 to 10, grid lines, origin at (0,0))

Explanation:

Step1: Identify slope and y-intercept

The equation is \( y = \frac{1}{4}x \), which is in slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. Here, \( m=\frac{1}{4} \) and \( b = 0 \). So the y - intercept is at the point \( (0,0) \).

Step2: Use slope to find another point

The slope \( m=\frac{1}{4} \) means "rise over run", or \( \frac{\text{change in }y}{\text{change in }x}=\frac{1}{4} \). Starting from the y - intercept \( (0,0) \), if we move 4 units to the right (change in \( x = 4 \)), we move 1 unit up (change in \( y=1 \)). So we get the point \( (0 + 4,0+1)=(4,1) \). We can also find other points, for example, if we move 8 units to the right from \( (0,0) \), we move 2 units up, getting \( (8,2) \), or move 4 units to the left (change in \( x=- 4 \)) and 1 unit down (change in \( y = - 1 \)) to get \( (-4,-1) \).

Step3: Plot the points and draw the line

Plot the points we found, such as \( (0,0) \), \( (4,1) \), \( (8,2) \), \( (-4,-1) \) on the coordinate plane and then draw a straight line through them.

Answer:

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

1. Plot the y - intercept at \( (0,0) \).
2. Use the slope \( \frac{1}{4} \) to find other points (e.g., from \( (0,0) \), move 4 right and 1 up to \( (4,1) \), 8 right and 2 up to \( (8,2) \), etc.).
3. Draw a straight line through the plotted points.