Question

a tiling company completes two jobs. the first job has $1200 in labor expenses for 40 hours worked, while the second job has $1560 in labor expenses for 52 hours worked. the relationship between the labor expenses and the hours worked is linear. which equation can be used to calculate the y-intercept of the linear equation?

\\(1200 = 40(40) + b\\)
\\(1560 = 30(40) + b\\)
\\(1560 = 30(52) + b\\)
\\(1200 = 52(30) + b\\)

Explanation:

Calculate the rate of change

Using the Slope of a Line knowledge point

$$ m = \frac{1560 - 1200}{52 - 40} = \frac{360}{12} = 30 $$

Formulate the linear equation

Using the Slope-Intercept Form knowledge point

$$ y = 30x + b $$

Substitute a known data point

Using the Slope-Intercept Form knowledge point

$$
LATEXBLOCK0
$$

Answer:

• (A) \(1200 = 40(40) + b\)
• (B) \(1560 = 30(40) + b\)
• (C) \(1560 = 30(52) + b\) (Correct answer)
• (D) \(1200 = 52(30) + b\)