Question

1. daniel works as a volunteer in a homeless shelter. so far, he has worked 22 hours, and he plans to continue working 3 hours per week. his hours worked as a function of time is shown in the graph. a. write an equation that represents the hours daniel will work as a function of time. ____________ b. identify the slope and y - intercept and describe their meanings. __________ __________ c. find the number of hours worked after 16 weeks. ____________ copyright © by holt, rinehart and winston. all rights reserved. 36 holt algebra 1

Explanation:

Step1: Determine the linear - equation form

The general form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Daniel has already worked 22 hours (initial value) and works 3 hours per week (rate of change). Let $y$ be the total number of hours worked and $x$ be the number of weeks. So the equation is $y=3x + 22$.

Step2: Identify slope and y - intercept

The slope $m = 3$. It means Daniel works 3 additional hours per week. The y - intercept $b = 22$, which represents the number of hours Daniel had already worked before he started counting the weeks.

Step3: Calculate hours after 16 weeks

Substitute $x = 16$ into the equation $y=3x + 22$. So $y=3\times16+22$. First, calculate $3\times16 = 48$. Then $y=48 + 22=70$.

Answer:

a. $y = 3x+22$
b. Slope $m = 3$, means 3 hours worked per week; y - intercept $b = 22$, means 22 hours already worked.
c. 70 hours