Straight Lines/Standard Curves
A straight line has only one slope or gradient
A straight-line graph is a special type of curve. It has the same slope everywhere so when determining the slope, it does not matter where in the line you calculate it.
For example, to find out how much a Lab Tech makes per hour, there are several ways to do it.
- You could measure how much they made in any single hour – such as they made $60 in two hours therefore $30 per hour.
If you want to get fancy, you could pick a different hour, but it seems more work for the same answer. For example, between hours 2 and 3, the Lab Tech earned $90 – $60 = $30 extra dollars: Remember when people want to find a slope, they often draw a figure that looks like that indicated in the graph below. This is will result in the same value for the rate of pay.
Hint: As long as the line goes through (0,0), it’s much easier to find the slope by just finding the value of y at a particular x value and dividing y by x. Remember what you are determining is the slope or gradient of the line.
What is the pay rate for the forest conservation worker? How about the veterinarian?
(All wage data taken from Monster.com)
(To make this problem interactive, turn on javascript!)
- I need a hint ... : It's not really possible to see (the value of the paycheck)at x = 1 hour. So pick a bigger x value, like x = 10 hr.
- ...another hint ... : If the forester works 10 hours, she makes 220 dollars...
- ...another hint ... : 220 dollars / 10 hours = ? dollars / 1 hour
- ...another hint ... : Now do the same for the vet...
I think I have the answer:
Forester = $22/hr,
Veterinarian = $42/hr
You may remember from high school that the equation of a straight line is:
The slope (known as ‘m’) is that rate or gradient we were talking about. The intercept (b) is just the value for y where the line crosses the y axis.