Question
Peyton steers a remote-control car. The equation y = 3x + 4 can be used to find y, the car’s distance from Peyton in feet, after x seconds.
Identify the y-intercept. What does it tell you about the car?
The y-intercept is ___. It tells you the car starts ___ feet from Peyton.
Identify the y-intercept. What does it tell you about the car?
The y-intercept is ___. It tells you the car starts ___ feet from Peyton.
Answers
GPT-4o mini
The y-intercept of the equation \( y = 3x + 4 \) is the value of \( y \) when \( x = 0 \).
To find the y-intercept, substitute \( x = 0 \):
\[
y = 3(0) + 4 = 4
\]
Thus, the y-intercept is **4**.
It tells you the car starts **4** feet from Peyton.
To find the y-intercept, substitute \( x = 0 \):
\[
y = 3(0) + 4 = 4
\]
Thus, the y-intercept is **4**.
It tells you the car starts **4** feet from Peyton.
Peyton steers a remote-control car. The equation y = 3x + 4 can be used to find y, the car’s distance from Peyton in feet, after x seconds.
Identify the y-intercept. What does it tell you about the car’s distance from Peyton after 1 second?
The slope is ___. After 1 second, the car’s distance ____ by ___ feet.
Identify the y-intercept. What does it tell you about the car’s distance from Peyton after 1 second?
The slope is ___. After 1 second, the car’s distance ____ by ___ feet.
GPT-4o mini
To analyze the equation \( y = 3x + 4 \):
1. **Y-Intercept**: As previously calculated, the y-intercept is **4**. This means that at \( x = 0 \), the car starts **4** feet from Peyton.
2. **Slope**: The slope is the coefficient of \( x \), which is **3**. This indicates that for every additional second, the distance of the car from Peyton increases by 3 feet.
Now, let's determine the car's distance after 1 second:
To find the distance \( y \) after \( x = 1 \):
\[
y = 3(1) + 4 = 3 + 4 = 7
\]
So after 1 second, the car's distance from Peyton is **7** feet.
The statement can be completed as follows:
The slope is **3**. After 1 second, the car’s distance **increases** by **3** feet (from 4 feet to 7 feet).
1. **Y-Intercept**: As previously calculated, the y-intercept is **4**. This means that at \( x = 0 \), the car starts **4** feet from Peyton.
2. **Slope**: The slope is the coefficient of \( x \), which is **3**. This indicates that for every additional second, the distance of the car from Peyton increases by 3 feet.
Now, let's determine the car's distance after 1 second:
To find the distance \( y \) after \( x = 1 \):
\[
y = 3(1) + 4 = 3 + 4 = 7
\]
So after 1 second, the car's distance from Peyton is **7** feet.
The statement can be completed as follows:
The slope is **3**. After 1 second, the car’s distance **increases** by **3** feet (from 4 feet to 7 feet).