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Answer :
To graph the equation [tex]\(y = -10x + 3000\)[/tex], you can follow these steps:
1. Understand the Equation:
The equation [tex]\(y = -10x + 3000\)[/tex] represents a linear function. Here, [tex]\(y\)[/tex] is the height of the skydiver in feet, and [tex]\(x\)[/tex] is the time in seconds. The coefficient -10 indicates the rate at which the skydiver descends, which is 10 feet per second. The constant 3000 represents the initial height from which the skydiver begins.
2. Identify Important Points:
- The y-intercept is at (0, 3000). This is where the skydiver starts, at 3000 feet when [tex]\(x = 0\)[/tex].
- To find when the skydiver reaches the ground ([tex]\(y = 0\)[/tex]), set the equation to zero:
[tex]\[
0 = -10x + 3000
\][/tex]
Solving for [tex]\(x\)[/tex],
[tex]\[
10x = 3000 \quad \Rightarrow \quad x = 300
\][/tex]
So, another point is (300, 0).
3. Sketch the Graph:
- Plot the y-intercept (0, 3000) on your graph.
- Plot the point where it reaches the ground (300, 0).
- Draw a line through these two points.
4. Label the Axes and Line:
- The x-axis represents time in seconds, and the y-axis represents height in feet.
- The line should be labeled as "Height over time".
5. Include Key Features:
- Since the line slope is negative, it should be angled downwards from left to right.
- Mark the point where the line crosses the x-axis, indicating where the skydiver lands.
This process helps you visualize how the skydiver's height decreases over time until she reaches the ground. If you want to practice, you could draw this graph with graph paper, or use graphing software to create a more precise plot.
1. Understand the Equation:
The equation [tex]\(y = -10x + 3000\)[/tex] represents a linear function. Here, [tex]\(y\)[/tex] is the height of the skydiver in feet, and [tex]\(x\)[/tex] is the time in seconds. The coefficient -10 indicates the rate at which the skydiver descends, which is 10 feet per second. The constant 3000 represents the initial height from which the skydiver begins.
2. Identify Important Points:
- The y-intercept is at (0, 3000). This is where the skydiver starts, at 3000 feet when [tex]\(x = 0\)[/tex].
- To find when the skydiver reaches the ground ([tex]\(y = 0\)[/tex]), set the equation to zero:
[tex]\[
0 = -10x + 3000
\][/tex]
Solving for [tex]\(x\)[/tex],
[tex]\[
10x = 3000 \quad \Rightarrow \quad x = 300
\][/tex]
So, another point is (300, 0).
3. Sketch the Graph:
- Plot the y-intercept (0, 3000) on your graph.
- Plot the point where it reaches the ground (300, 0).
- Draw a line through these two points.
4. Label the Axes and Line:
- The x-axis represents time in seconds, and the y-axis represents height in feet.
- The line should be labeled as "Height over time".
5. Include Key Features:
- Since the line slope is negative, it should be angled downwards from left to right.
- Mark the point where the line crosses the x-axis, indicating where the skydiver lands.
This process helps you visualize how the skydiver's height decreases over time until she reaches the ground. If you want to practice, you could draw this graph with graph paper, or use graphing software to create a more precise plot.
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