Question

in the table below, x represents miles traveled and y represents the cost to travel by train.

which linear equation represents the situation?

\\(y = 2x + 8.50\\)
\\(y = 2.25x + 4.00\\)
\\(y = 6.50x + 2.25\\)
\\(y = 12x + 22.50\\)

Explanation:

Calculate the rate of change

Using the Linear Equation from Table and Slope-Intercept Form knowledge points

$$ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{15.25 - 8.50}{5 - 2} = \frac{6.75}{3} = 2.25 $$

Determine the initial value

Using the Slope-Intercept Form knowledge point

$$
LATEXBLOCK0
$$

Formulate the linear equation

Using the Slope-Intercept Form knowledge point

$$ y = 2.25x + 4.00 $$

Answer:

• (A) \(y = 2x + 8.50\)
• (B) \(y = 2.25x + 4.00\) (Correct answer)
• (C) \(y = 6.50x + 2.25\)
• (D) \(y = 12x + 22.50\)