Question

graph the line.
y=2x

Explanation:

Step1: Identify the slope-intercept form

The equation \( y = 2x \) is in slope - intercept form \( y=mx + b \), where \( m = 2 \) (slope) and \( b = 0 \) (y - intercept). So the line passes through the origin \((0,0)\).

Step2: Find another point

Using the slope \( m=\frac{\text{rise}}{\text{run}}=2=\frac{2}{1}\). From the point \((0,0)\), we move 1 unit to the right (run = 1) and 2 units up (rise = 2). This gives us the point \((1,2)\).

Step3: Graph the line

Plot the points \((0,0)\) and \((1,2)\) (and other points like \((2,4)\), \((- 1,-2)\) etc. for accuracy) and then draw a straight line passing through these points.

(Note: Since the problem is about graphing, the final answer is the graph of the line \( y = 2x \) passing through the origin with a slope of 2. If we were to describe the key points, the line passes through \((0,0)\) and \((1,2)\) and extends infinitely in both directions with a positive slope of 2.)

Answer:

The line \( y = 2x \) is graphed by plotting the points \((0,0)\), \((1,2)\), \((2,4)\) etc. and drawing a straight line through them. The line has a slope of 2 and passes through the origin.