Question

In 1991, minimum wage was $4.25 per hour; in 1997, minimum wage increased in $5.15 per hour. Find the rate of change in the minimum wage per year from 1991 to 1997.

Answer 1

The rate of change in the minimum wage from 1991 to 1997 was $0.15 per year, calculated by dividing the wage increase of $0.90 by the number of years, which is six.

Step-by-step explanation:

To find the rate of change in the minimum wage per year between 1991 and 1997, we need to calculate the difference in minimum wage between these years and then divide by the number of years that have passed. The minimum wage increased from $4.25 in 1991 to $5.15 in 1997.

First, calculate the change in minimum wage: $5.15 (1997) - $4.25 (1991) = $0.90.

Next, determine the number of years that have passed: 1997 - 1991 = 6 years.

Finally, calculate the rate of change per year: Rate of change = Change in minimum wage / Number of years = $0.90 / 6 years = $0.15 per year.

Therefore, the rate of change in the minimum wage from 1991 to 1997 was $0.15 per year.

Answer 2

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

`\begin{array} \cline{1-2} \stackrel{x}{year}&\stackrel{y}{wage}\\ \cline{1-2} 1991&4.25\\ 1997&5.15\\ \cline{1-2} \end{array} \hspace{5em} (\stackrel{x_1}{1991}~,~\stackrel{y_1}{4.25})\qquad (\stackrel{x_2}{1997}~,~\stackrel{y_2}{5.15}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5.15}-\stackrel{y1}{4.25}}}{\underset{run} {\underset{x_2}{1997}-\underset{x_1}{1991}}} \implies \cfrac{0.90}{6}\implies \cfrac{0.15}{1}\implies 0.15~(\$)/(year)`