During the period 1990-2004 the average commute to work in the greater washington, d.c area increased from 20 minutes in 1990 (t=0) by an average of 3 minutes per year. Use these data to express y, the average number of minutes commuting to work, as a linear function of x, the number of years since 1990.
I set it up as y=3t+20t
almost. why 20t?
To express y, the average number of minutes commuting to work, as a linear function of x, the number of years since 1990, we need to determine the equation of the line.
Given that the average commute in 1990 (t=0) was 20 minutes and increased by 3 minutes per year, we can use the slope-intercept form of a linear equation:
y = mx + b,
where m represents the slope of the line and b represents the y-intercept.
In this case, the slope (m) is the rate of increase in minutes per year, which is 3 minutes. The y-intercept (b) is the value of y when x is 0, which is 20 minutes.
Plugging these values into the equation, we get:
y = 3x + 20.
Therefore, the linear function representing the average number of minutes commuting to work (y) as a function of the number of years since 1990 (x) is y = 3x + 20.