Rates & proportional relationships example
About this video
Sal compares the unit rate of the equation y = 6.5x with the unit rate of a graphed line. The unit rate is how much y changes when x increases by 1: 6.5 for the equation and about 3.5 for the graph, so the graph's unit rate is less.
You'll be able to
- find the unit rate from an equation of the form y = kx.
- read the unit rate from a graph by seeing how much y changes when x increases by 1.
- compare unit rates shown in different ways.
Key words
- unit rate
- How much one quantity changes when the other changes by exactly 1.
- rate of change
- How fast y changes compared to x.
Transcript
Which is less-- the unit rate of the equation y equals 6.5x or the unit rate of the graph shown below? So when they're talking about unit rate-- and they're actually a little bit ambiguous here. They should have been clearer in this question. I'm assuming they're asking us about the unit rate at which y changes with respect to x.
Or how much does y change for a change of 1 in x, the unit rate. And over here, you see when x changes 1, y is going to change by 6.5. Every time x increases by 1, y is going to increase by 6.5. Or you could say the unit rate of change of y with respect to x is 6.5 for every 1 change in x.
In this graph right over here, as x changes 1, as x increases 1, y increases it looks like by about 3 and 1/2. x increases by 1, y increases by 3 and 1/2. So the unit rate of change here of y with respect to x is 3 and 1/2 for every unit increase in x. So this line is increasing at a slower rate than this equation.
Or y in this line is increasing at a slower rate with respect to x than y is increasing with respect to x in this equation right over here. So the unit rate of the graph is less than the unit rate of the equation.
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