Question

a car is taken to a mechanic for repair. the mechanic charges 115 dollars for parts, plus 34 dollars per hour for labor.

write a linear equation, in slope-intercept form, that models this situation.
(note: \y =\ is already given -- just enter the right side of the equation.)
y =

in the equation, the variable x represents which of the following? (choose one)
○ time spent repairing the vehicle (hours)
○ hourly cost of labor (dollars per hour)
○ total cost of the repair (dollars)
○ cost for parts (dollars)

Explanation:

Part 1: Writing the linear equation

Step1: Recall slope - intercept form

The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope (rate of change) and $b$ is the y - intercept (initial value).

Step2: Identify $m$ and $b$

The cost for parts ($115$ dollars) is the initial value ($b$), and the cost per hour for labor ($34$ dollars per hour) is the rate of change ($m$). If $x$ is the number of hours of labor, then the total cost $y$ is given by the sum of the cost of parts and the cost of labor. The cost of labor is $34x$ (since it's $34$ dollars per hour times $x$ hours), and the cost of parts is $115$. So the equation is $y=34x + 115$. Since we only need the right - hand side, it is $34x + 115$.

Step3: Determine what $x$ represents

The variable $x$ is multiplied by the hourly labor cost ($34$). The hourly labor cost is a rate, and when we multiply a rate by time, we get the total cost of labor. So $x$ represents the time spent repairing the vehicle (hours). The hourly cost of labor is $34$ (a constant, not $x$), the total cost of repair is $y$, and the cost for parts is $115$ (a constant, not $x$).

Answer:

(for the equation part): $34x + 115$