Question

graph the line.
y = 4x

Explanation:

Step1: Identify the slope-intercept form

The equation \( y = 4x \) is in the slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. Here, \( m = 4 \) and \( b=0 \). This means the line passes through the origin \((0,0)\) since when \( x = 0 \), \( y=4\times0 = 0\).

Step2: Find another point

We can find another point on the line by choosing a value for \( x \) and calculating the corresponding \( y \) value. Let's choose \( x = 1 \). Then \( y=4\times1=4 \), so the point \((1,4)\) is on the line.

Step3: Graph the line

Plot the points \((0,0)\) and \((1,4)\) on the coordinate plane. Then draw a straight line passing through these two points. We can also check with another point, for example, if \( x=- 1 \), then \( y = 4\times(-1)=-4 \), so the point \((-1,-4)\) is also on the line, which can be used to verify the line.

(Note: Since the problem is about graphing, the final answer is the graph of the line \( y = 4x \) passing through the origin and points like \((1,4)\), \((- 1,-4)\) etc. But in text - based form, we can describe the process of graphing as above.)

Answer:

To graph \( y = 4x \):

1. Recognize it has a y - intercept of \( 0 \), so it passes through \((0,0)\).
2. Use the slope \( 4=\frac{4}{1}\) (rise over run) to find another point: from \((0,0)\), move 1 unit right (run) and 4 units up (rise) to get \((1,4)\).
3. Draw a straight line through \((0,0)\) and \((1,4)\) (and other points like \((-1,-4)\) for verification). The line \( y = 4x \) is a straight line passing through the origin with a steep positive slope.