QuestionThe minimum hourly wage, $y$ (in dollars per hour), in a country can be approximated by the equation $y=0.16 x+2.63$ . In this equation, $x$ represents the number of years since 1970 ( $x=0$ represents 1970, $x=5$ represents 1975, and so on).
Federal Minimum Hourly Wage by Year
Part 1 of 4 (a) Use the equation to approximate the minimum wage in the year 1975.
The minimum wage in 1975 was approximately $\$ 3.43$ . $\square$
Part 2 of 4 (b) Use the equation to estimate the minimum wage in the year 1995.
The minimum wage in 1995 was approximately $\$ 6.63$ .
Part: $2 / 4$
Part 3 of 4 (c) Determine the $y$ -intercept. Interpret the meaning of the $y$ -intercept in the context of this problem.
The $y$ -intercept is $\square$ $\square$ . In the year $\square$ the minimum wage was approximately $\$$ $\square$ per hour.

Studdy Solution

STEP 1

1. The equation for the minimum hourly wage is given by $y = 0.16x + 2.63$ .
2. $x$ represents the number of years since 1970.
3. We need to find the minimum wage for specific years and interpret the $y$ -intercept.

STEP 2

1. Calculate the minimum wage for the year 1975.
2. Calculate the minimum wage for the year 1995.
3. Determine and interpret the $y$ -intercept.

STEP 3

Calculate the minimum wage for the year 1975.
Since $x = 5$ for the year 1975, substitute $x = 5$ into the equation:
$y = 0.16(5) + 2.63$
Calculate:
$y = 0.80 + 2.63$ $y = 3.43$
The minimum wage in 1975 was approximately $\$3.43$ .

STEP 4

Calculate the minimum wage for the year 1995.
Since $x = 25$ for the year 1995, substitute $x = 25$ into the equation:
$y = 0.16(25) + 2.63$
Calculate:
$y = 4.00 + 2.63$ $y = 6.63$
The minimum wage in 1995 was approximately $\$6.63$ .

STEP 5

Determine and interpret the $y$ -intercept.
The $y$ -intercept occurs when $x = 0$ .
Substitute $x = 0$ into the equation:
$y = 0.16(0) + 2.63$ $y = 2.63$
The $y$ -intercept is $2.63$ .
Interpretation: In the year 1970, the minimum wage was approximately $\$2.63$ per hour.

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