Question

(a) a person is paying $19.40 per week to a friend to repay a $194 loan.
the situation matches graph ? ▼. the slope is , which represents the decrease in the —select— of the loan each week. the y-intercept is
$(x,y) = \left(\\ \\ \\ \\ \\ \\ \\ \\ \\ \
ight)$, which represents the —select— of the loan.

(b) an employee is paid $10.50 per hour plus $2 for each unit produced per hour.
the situation matches graph —select— ▼. the slope is , which represents the —select— hourly wage per unit produced. the y-intercept is
$(x,y) = \left(\\ \\ \\ \\ \\ \\ \\ \\ \\ \
ight)$, which represents the —select— hourly wage.

(c) a sales representative receives $30 per day for food plus $0.39 for each mile traveled.
the situation matches graph —select— ▼. the slope is , which represents the increase in —select— . the y-intercept is $(x,y) = \left(\\ \\ \\ \\ \\ \\ \\ \\ \\ \
ight)$,
which represents the —select—

(d) a computer that was purchased for $765 depreciates $100 per year.
the situation matches graph —select— ▼. the slope is , which represents the decrease in the —select— of the computer each year. the y-intercept is
$(x,y) = \left(\\ \\ \\ \\ \\ \\ \\ \\ \\ \
ight)$, which represents the —select— of the computer.

Explanation:

Step1: Analyze part (a) linear model

Let $x$ = weeks, $y$ = remaining loan.
Initial loan: $y(0)=194$, weekly payment: $19.40$.
Slope: $-19.40$ (decrease per week), y-intercept: $(0, 194)$ (initial loan).

Step2: Analyze part (b) linear model

Let $x$ = units produced, $y$ = hourly wage.
Base wage: $10.50$, per-unit bonus: $2$.
Slope: $2$ (wage increase per unit), y-intercept: $(0, 10.50)$ (base wage).

Step3: Analyze part (c) linear model

Let $x$ = miles traveled, $y$ = daily pay.
Base food pay: $30$, per-mile rate: $0.39$.
Slope: $0.39$ (pay increase per mile), y-intercept: $(0, 30)$ (base food pay).

Step4: Analyze part (d) linear model

Let $x$ = years, $y$ = computer value.
Initial value: $765$, annual depreciation: $100$.
Slope: $-100$ (value decrease per year), y-intercept: $(0, 765)$ (initial value).

Answer:

Part (a)

• Slope: $\boldsymbol{-19.40}$ (decrease in remaining amount of the loan each week)
• y-intercept: $\boldsymbol{(0, 194)}$ (represents the initial total amount of the loan)

Part (b)

• Slope: $\boldsymbol{2}$ (represents the additional hourly wage per unit produced)
• y-intercept: $\boldsymbol{(0, 10.50)}$ (represents the base hourly wage)

Part (c)

• Slope: $\boldsymbol{0.39}$ (represents the increase in daily total pay)
• y-intercept: $\boldsymbol{(0, 30)}$ (represents the base daily food pay)

Part (d)

• Slope: $\boldsymbol{-100}$ (decrease in the remaining value of the computer each year)
• y-intercept: $\boldsymbol{(0, 765)}$ (represents the initial purchase value of the computer)

(Note: Graph matches are not solvable without graph images, but the numerical and interpretive values above are complete.)