The Question I need help with is below

Question

The data below represents the federal minimum hourly wage for various years.

Year (x) 1980 1985 1990 1995 2000 2005 2010
Wage (y) 3.10 3.35 3.80 4.25 5.15 5.15 7.25

6. Find the slope of the line between 1980 and 1990.
7. Find the slope of the line between 1980 and 2000.
8. Find the slope of the line between 1980 and 2010.
9. Write the equation of the line between the first (1980, 3.10) and the last (2010, 7.25) data.

Answer 1

Slope is rise/run, or (change in y) / (change in x). So, from 1980 to 1990:

 

(3.8 - 3.1) / (1990 - 1980) = 0.7/10 = 0.07

 

From 1980 to 2000:

 

(5.15 - 3.1) / (2000 - 1980) = 2.05/20 = 0.1025

 

From 1980 to 2010:

 

(7.25 - 3.1) / (2010 - 1980) = 4.15/30 = 0.1383

 

 

That last slope is the one you'll use for the equation of the line between (1980, 3.1) and (2010, 7.25). Use point-slope form, where m = slope = 0.1383 and (x₁, y₁) = point on the line = (2010, 7.25):

 

y - y₁ = m(x - x₁)

y - 7.25 = 0.1383(x - 2010)

 

You can put that into slope-intercept form (y = mx + b) if you'd like:

 

y = 0.1383(x - 2010) + 7.25

y = 0.1383x - 277.983 + 7.25

y = 0.1383x - 285.233