Question

graph the line.

$y = 3x$

Explanation:

Step1: Identify the form of the equation

The equation \( y = 3x \) is in the slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. Here, \( m = 3 \) and \( b=0 \), so the line passes through the origin \((0,0)\).

Step2: Find another point

We can choose a value for \( x \) and find the corresponding \( y \) value. Let's take \( x = 1 \). Substitute \( x = 1 \) into the equation \( y=3x \), we get \( y=3\times1 = 3 \). So the point \((1,3)\) is on the line.

Step3: Plot the points and draw the line

First, plot the point \((0,0)\) (the origin) and the point \((1,3)\) on the coordinate plane. Then, use a straight - edge to draw a line through these two points. We can also find more points for accuracy. For example, if \( x = 2 \), then \( y=3\times2 = 6 \), so the point \((2,6)\) is on the line; if \( x = 3 \), then \( y = 3\times3=9 \), so the point \((3,9)\) is on the line. Plotting these additional points and drawing a line through them will give the graph of \( y = 3x \).

Answer:

To graph \( y = 3x \):

1. Plot the point \((0,0)\) (since when \( x = 0 \), \( y=3\times0 = 0\)).
2. Plot other points by substituting values of \( x \) into the equation (e.g., \( x = 1\), \( y = 3\) gives \((1,3)\); \( x = 2\), \( y = 6\) gives \((2,6)\); etc.).
3. Draw a straight line through the plotted points. The line passes through the origin and has a slope of 3, rising 3 units for every 1 unit it moves to the right along the x - axis.