Question

graph the line.
y = 3x

Explanation:

Step1: Identify the slope - intercept form

The equation of the line is given in the slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For the equation \(y=3x\), we can rewrite it as \(y = 3x+0\). So, the slope \(m = 3\) (which can be written as \(\frac{3}{1}\)) and the y - intercept \(b = 0\). This means the line passes through the origin \((0,0)\).

Step2: Find another point using the slope

The slope \(m=\frac{\text{rise}}{\text{run}}=\frac{3}{1}\). Starting from the point \((0,0)\) (the y - intercept), we move up 3 units (rise) and 1 unit to the right (run). So, if we move up 3 units from \(y = 0\) and right 1 unit from \(x = 0\), we get the point \((0 + 1,0+3)=(1,3)\). We can also find a point on the left side of the origin. Using the slope \(\frac{- 3}{-1}\) (since a negative divided by a negative is positive), starting from \((0,0)\), we move down 3 units (rise=- 3) and left 1 unit (run = - 1), we get the point \((0-1,0 - 3)=(-1,-3)\).

Step3: Plot the points and draw the line

Plot the points \((0,0)\), \((1,3)\) and \((-1,-3)\) on the coordinate plane. Then, draw a straight line passing through these points.

To graph the line \(y = 3x\):

1. Recognize that the y - intercept \(b = 0\), so the line passes through \((0,0)\).
2. Use the slope \(m = 3=\frac{3}{1}\) to find another point. From \((0,0)\), move 1 unit to the right (run = 1) and 3 units up (rise = 3) to get the point \((1,3)\). Or move 1 unit to the left (run=-1) and 3 units down (rise = - 3) to get \((-1,-3)\).
3. Plot the points \((0,0)\), \((1,3)\), \((-1,-3)\) and draw a straight line through them.

(Note: Since the question is about graphing, the final answer is the graph of the line passing through \((0,0)\), \((1,3)\), \((-1,-3)\) etc. with a slope of 3)

Answer:

The line \(y = 3x\) is a straight line passing through the origin \((0,0)\) with a slope of 3. To graph it, plot the points \((0,0)\), \((1,3)\), \((-1,-3)\) (and other points found using the slope) and draw a straight line through them.