Question

Leticia was driving 45 miles per hour.

After traveling for 4 hours, she found that she was 250 miles east of Albertville.

Identify the given values.

x = the number of hours driven = "4 hours

y the distance traveled 250 miles

m = rate of change = '45 miles per hour

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

Then solve the equation.

y = mx + b

*blank 1*

*blank 2*

*blank 3*


Options for blank 1

A 45 = (250)(4) + b

B 250 = (45)(4) + b

C 4 = (250)(45) + b

Options for blank 2

A 45 = 1000 + b

B 250 = 180 + b

C 4 = 11250 + b

Options for blank 3

A 11, 246 = b

B 70 = b

C 955 = b

Answer 1

To formulate the equation in the form \( y = mx + b \), we can identify the variables based on the given values:

- \( y \) is the total distance traveled (in this case, \( 250 \) miles).
- \( m \) is the rate of change, which is the speed (in this case, \( 45 \) miles per hour).
- \( x \) is the number of hours driven (in this case, \( 4 \) hours).
- \( b \) is the y-intercept, which in this context would represent the starting distance from Albertville (which is \( 0 \) miles since she starts driving from the location).

Thus, we can substitute these into the equation:

1. Substitute \( y = 250 \), \( m = 45 \), and \( x = 4 \) into the equation:
\[
250 = 45(4) + b
\]

**Blank 1:**
So, the first blank will be:
**B 250 = (45)(4) + b**

2. Now, calculate \( 45(4) \):
\[
45(4) = 180
\]
Substitute that value back into the equation:
\[
250 = 180 + b
\]

**Blank 2:**
Thus, the second blank will be:
**B 250 = 180 + b**

3. To solve for \( b \), subtract \( 180 \) from both sides:
\[
b = 250 - 180 = 70
\]

**Blank 3:**
So, the final value for \( b \) will be:
**B 70 = b**

Putting everything together:
- **Blank 1:** B 250 = (45)(4) + b
- **Blank 2:** B 250 = 180 + b
- **Blank 3:** B 70 = b