Question

1. every 2 seconds, a ballon rises 1 meter. using the equation y = 2x, draw a graph of the proportional relationship. label the graph.

Explanation:

Step1: Identify the equation and variables

The equation is \( y = 2x \), where \( x \) is time in seconds and \( y \) is the height of the balloon in meters. We need to find points \((x,y)\) that satisfy this equation.

Step2: Find key points

• When \( x = 0 \), \( y = 2(0)=0 \), so the point is \((0,0)\).
• When \( x = 2 \), \( y = 2(2) = 4 \)? Wait, no, wait the problem says every 2 seconds, the balloon rises 1 meter. Wait, maybe there's a misinterpretation. Wait the problem says "Every 2 seconds, a balloon rises 1 meter" but the equation given is \( y = 2x \). Wait, maybe the equation is \( y=\frac{1}{2}x \)? Wait no, let's re - read. Wait the user's problem says "Using the equation \( y = 2x \), draw a graph of the proportional relationship". Let's proceed with the given equation \( y = 2x \).
• When \( x=1 \), \( y = 2(1)=2 \)
• When \( x = 2 \), \( y=2(2) = 4 \)
• When \( x=3 \), \( y = 2(3)=6 \)
• When \( x = 4 \), \( y=2(4)=8 \)
• When \( x=5 \), \( y = 2(5)=10 \)

Step3: Plot the points

On the given grid, the x - axis (horizontal) is labeled from 0 - 10 (time in seconds) and the y - axis (vertical) is labeled from 0 - 10 (height in meters). Plot the points \((0,0)\), \((1,2)\), \((2,4)\), \((3,6)\), \((4,8)\), \((5,10)\). Then draw a straight line passing through these points since it's a proportional relationship (a straight line through the origin for \( y = kx \) where \( k\) is the constant of proportionality).

Answer:

To draw the graph of \( y = 2x \):

1. Plot the point \((0,0)\) (when time \( x = 0\) seconds, height \( y = 0\) meters).
2. Plot the point \((1,2)\) (when \( x = 1\) second, \( y=2\times1 = 2\) meters).
3. Plot the point \((2,4)\) (when \( x = 2\) seconds, \( y = 2\times2=4\) meters).
4. Continue plotting points like \((3,6)\), \((4,8)\), \((5,10)\) (for \( x = 3,4,5\) respectively).
5. Draw a straight line passing through all these plotted points. The line should pass through the origin \((0,0)\) and have a slope of 2 (rise 2 units for every 1 unit run in the x - direction).