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.

Question

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.

Answer 1

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.

Answer 2

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.

Answer 3

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).