Question

x = the number of hours driven = `4 hours`

y = the distance traveled = `250 miles`

m = the rate of change = `45 miles per hour`

Use the given values to write an equation in y = mx + b form.
Then solve the equation.

Answer 1

To write the equation in the form \( y = mx + b \), we need to identify the variables and the values given:

- \( x \) represents the number of hours driven.
- \( y \) represents the distance traveled.
- \( m \) is the rate of change (the slope), which is \( 45 \) miles per hour.
- \( b \) is the y-intercept.

Since the rate of change is given (45 miles per hour), we can write the equation. We'll also need to determine the y-intercept \( b \).

From the information, we know that after driving for 4 hours, the distance traveled is 250 miles. We can use this information to find \( b \):

1. Substitute \( x = 4 \) and \( y = 250 \) into the equation \( y = mx + b \):

\[
250 = 45(4) + b
\]

2. Calculate \( 45(4) \):

\[
250 = 180 + b
\]

3. Solve for \( b \):

\[
b = 250 - 180
\]
\[
b = 70
\]

Now we can write the full equation:

\[
y = 45x + 70
\]

This equation represents the distance traveled as a function of the hours driven, with a baseline distance (the y-intercept) of 70 miles when no driving occurs.

### Solving the equation

Now, if we solve the equation for different values of \( x \), we can predict the distance traveled \( y \) for any given number of hours. For example, if you wanted to find out the distance traveled if someone drives for 6 hours:

1. Substitute \( x = 6 \) into the equation:

\[
y = 45(6) + 70
\]

2. Calculate \( 45(6) \):

\[
y = 270 + 70
\]
\[
y = 340
\]

So, if someone drives for 6 hours, they would travel 340 miles according to the equation \( y = 45x + 70 \).