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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

1 answer

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

  1. 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

  1. 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