Slope
Before we think of slope as a rate of change, we first have to understand what a rate is.
Think of some common rates:
miles per hour, $ each day, rotations per minute,
Basically, a rate is something that defines the relationship between two things. If we talk about the previous examples, we could say that the rate of "miles per hour" tells me how many miles I can travel in an hour. Likewise, the rate of "$ each day" tells me how much money I can make in a day. Once I understand what a rate means I can then apply it to the idea of "slope".
The slope of a line is often described as a rate of change. For example, if I make $365 every 2 days then my rate could be represented as 365/2. I can then use this rate to find out how much money I will make in a month or whatever value of time I'm interested in. There are endless read world examples where slopes can be defined as rates of change.
Hint: When reading a real world situation look for the words every,each, in, or per to help you identify the slope (rate of change).
Write the slope in fraction form for the following real world examples. Then click below to check your answers.
Fernando makes $15 an hour at his new job.
Jane eats 3 apples every week. (write the slope in apples per day)
Alex paints four rooms in eleven days.
Sarah drives fast on the highway. She was clocked at 96 miles per hour last night.
John watches five movies every three weeks.
When I went to the doctor he told me that my heart beat 12 times in 10 seconds. How many beats per minute is that?
Before we think of slope as a rate of change, we first have to understand what a rate is.
Think of some common rates:
miles per hour, $ each day, rotations per minute,
Basically, a rate is something that defines the relationship between two things. If we talk about the previous examples, we could say that the rate of "miles per hour" tells me how many miles I can travel in an hour. Likewise, the rate of "$ each day" tells me how much money I can make in a day. Once I understand what a rate means I can then apply it to the idea of "slope".
The slope of a line is often described as a rate of change. For example, if I make $365 every 2 days then my rate could be represented as 365/2. I can then use this rate to find out how much money I will make in a month or whatever value of time I'm interested in. There are endless read world examples where slopes can be defined as rates of change.
Hint: When reading a real world situation look for the words every,each, in, or per to help you identify the slope (rate of change).
Write the slope in fraction form for the following real world examples. Then click below to check your answers.
Fernando makes $15 an hour at his new job.
Jane eats 3 apples every week. (write the slope in apples per day)
Alex paints four rooms in eleven days.
Sarah drives fast on the highway. She was clocked at 96 miles per hour last night.
John watches five movies every three weeks.
When I went to the doctor he told me that my heart beat 12 times in 10 seconds. How many beats per minute is that?