Cost of Tuition In 2000, the average cost of tuition and fees at private four-year colleges was $16,200, and in 2005 it was $20,100. Sketch a line that passes through the points (2000, 16200) and (2005, 20100).
To sketch a line passing through two given points (2000, 16200) and (2005, 20100), we can use the slope-intercept form of a linear equation, y = mx + b, where y represents the dependent variable (tuition cost in this case), x represents the independent variable (year), m represents the slope of the line, and b represents the y-intercept.
To find the slope (m), we can use the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the values from the points (2000, 16200) and (2005, 20100), we have:
m = (20100 - 16200) / (2005 - 2000)
m = 3900 / 5
m = 780
Now that we have the slope (m), we can use the point-slope form of a linear equation, which is:
y - y1 = m(x - x1)
Let's choose one point (2000, 16200) and substitute the values into the equation:
y - 16200 = 780(x - 2000)
Simplifying the equation, we have:
y - 16200 = 780x - 1560000
Rearranging the equation to slope-intercept form, we get:
y = 780x - 1560000 + 16200
y = 780x - 1543800
This is the equation of the line passing through the points (2000, 16200) and (2005, 20100).
To graph the line, we can plot the two given points and draw a line connecting them.