Question

graph the line $y = 3x$.

(there is a coordinate plane with a line drawn and a message saying neither of your points are on the correct line and thats not it. try again. score: 0%)

Explanation:

Step1: Identify the slope and y-intercept

The equation \( y = 3x \) is in slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. Here, \( m = 3 \) (which can be written as \( \frac{3}{1} \)) and \( b = 0 \). This means the line passes through the origin \((0,0)\) since when \( x = 0 \), \( y=3\times0 = 0\).

Step2: Find another point using the slope

The slope \( m=\frac{\text{rise}}{\text{run}}=\frac{3}{1} \). Starting from the point \((0,0)\), if we move 1 unit to the right (increase \( x \) by 1, run = 1) and 3 units up (increase \( y \) by 3, rise = 3), we get the point \((0 + 1,0+3)=(1,3)\). We can also find a point by substituting \( x=- 1\) into the equation: \( y=3\times(-1)=-3 \), so the point \((-1,-3)\) is also on the line.

Step3: Graph the line

Plot the points \((0,0)\) and \((1,3)\) (or \((-1,-3)\) and \((0,0)\)) and then draw a straight line passing through these points.

To graph \( y = 3x \) correctly:

1. Plot the point \((0,0)\) (because when \( x = 0 \), \( y=0\)).
2. Use the slope \( 3=\frac{3}{1} \). From \((0,0)\), move 1 unit to the right (to \( x = 1 \)) and 3 units up (to \( y = 3 \)) to plot the point \((1,3)\).
3. Draw a straight line through \((0,0)\) and \((1,3)\) (or other points like \((-1,-3)\) and \((0,0)\)).

Answer:

To graph \( y = 3x \):

• Plot the point \((0,0)\) (since the y - intercept \( b = 0\) and when \( x = 0\), \( y=0\)).
• Use the slope \( m = 3=\frac{3}{1}\). From \((0,0)\), move 1 unit right (run) and 3 units up (rise) to get the point \((1,3)\).
• Draw a straight line through \((0,0)\) and \((1,3)\) (additional points like \((-1,-3)\) can also be used for accuracy).