Question

problem 19
34 a landscaping company charges a set fee for a spring cleanup plus an hourly labor rate. the total cost is modeled by the function ( c(x) = 35x + 60 ). in this function, what does the 35 represent?

1. the set fee for the cleanup
2. the hourly labor rate for a cleanup
3. the profit earned by the company for one cleanup
4. the number of hours of labor required for one cleanup

f.if.b.4: graphing linear functions (linear equations)
problem 20
35 what is the ( y )-intercept of the line that passes through the points ( (-1, 5) ) and ( (2, -1) )?

1. ( -1 )
2. ( -2 )
3. ( 3 )
4. ( 5 )

a.rei.d.10: writing linear functions (linear equations)
problem 21
37 what is an equation of the line that passes through the points ( (2, 7) ) and ( (-1, 3) )?

1. ( y - 2 = \frac{3}{4}(x - 7) )
2. ( y - 2 = \frac{4}{3}(x - 7) )
3. ( y - 7 = \frac{3}{4}(x - 2) )
4. ( y - 7 = \frac{4}{3}(x - 2) )

Explanation:

Problem 19

Step1: Identify linear function form

The total cost follows $C(x)=mx+b$, where $m$ is the variable rate, $b$ is the fixed cost, and $x$ is hours.

Step2: Match values to the scenario

Here, $C(x)=35x+80$, so $35$ is multiplied by $x$ (hours), meaning it is the hourly rate.

Step1: Calculate slope of the line

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$.
$m=\frac{-1-5}{2-(-1)}=\frac{-6}{3}=-2$

Step2: Write point-slope form

Use point $(-1,5)$: $y-5=-2(x+1)$

Step3: Convert to slope-intercept form

Expand and solve for $y$:
$y-5=-2x-2$
$y=-2x+3$
The $y$-intercept is the constant term.

Step1: Calculate the slope

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$.
$m=\frac{3-7}{-1-2}=\frac{-4}{-3}=\frac{4}{3}$

Step2: Use point-slope form

Use point $(2,7)$: $y-y_1=m(x-x_1)$
Substitute values: $y-7=\frac{4}{3}(x-2)$

Answer:

1. the hourly labor rate for a cleanup

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Problem 35