Question

graph the line.
( y = 2x )

Explanation:

Step1: Identify the slope and y-intercept

The equation \( y = 2x \) is in slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. Here, \( m = 2 \) and \( b=0 \). This means the line passes through the origin \((0,0)\) and has a slope of 2 (for every 1 unit we move to the right along the x - axis, we move up 2 units along the y - axis).

Step2: Find two points on the line

• When \( x = 0 \), \( y=2(0)=0 \), so the point \((0,0)\) is on the line.
• When \( x = 1 \), \( y = 2(1)=2 \), so the point \((1,2)\) is on the line.
• When \( x=- 1 \), \( y=2(-1)=-2 \), so the point \((-1, - 2)\) is on the line.

Step3: Plot the points and draw the line

Plot the points \((0,0)\), \((1,2)\) (and/or \((-1,-2)\)) on the coordinate plane. Then, use a straightedge to draw a line through these points. The line should pass through the origin and have a positive slope, rising 2 units for each 1 - unit run to the right.

Answer:

To graph \( y = 2x \), plot the points \((0,0)\) and \((1,2)\) (or other points found using the equation) and draw a straight line through them. The line passes through the origin and has a slope of 2. (Note: Since the question is about graphing, the final answer is the graph of the line \( y = 2x \) as described in the steps, passing through \((0,0)\), \((1,2)\), \((-1,-2)\) etc., with a slope of 2.)