I am slightly confused about finding the rate of change from a graph.
When you pick the points to plug into the rate of change formula, do they have to be right next to each other?
The test material I have says that they can be ANY points on the graph (on the line), but when I apply that method I get the wrong answer. The only time I get the correct answer is when the points are right next to each other.
I really want to memorize the correct information, so any help is really appreciated!
@owlsaremybuddies In what context?
If the graph is a line in the xy-plane (I think this is what you mean), then any two distinct points will yield the same slope.
What problem is this? Are they asking for an average rate of change, expecting you to draw a line of best fit? Because while it is true that the points don’t matter if they are all on the line, it definitely matters when the points are two points in the neighborhood of the line of best fit. In that case, getting the “right” slope depends on picking the “right” points – or ignoring their points and using two points from your line of best fit instead.
But this is just a guess about what’s going on here. Tell us more about the problem…
Sorry I didn’t elaborate!
(I hope I can explain this correctly! This has been taken from Khan Academy’s SAT prep)
Here is the problem:
Karl filled up the tank of his truck and set out to deliver a shipment of bananas to Alaska. The graph above shows the amount of fuel, f, in liters, remaining in the truck’s tank after Karl has driven a distance of d kilometers. At what rate did Karl’s truck consume fuel, in liters per kilometer?
There is a graph with an arrow through point 500 on the y-axis and it goes through point 840ish on the x-axis. I chose two points that were clearly visible, but I got the answer wrong, and in the solution it shows different points being used. So I’m not sure what it means when it says you can use any points (in the solution.)
This is such a simple topic, I’m not sure why I am having problems figuring it out, lol!
(I hope this makes sense!)
@owlsaremybuddies If the graph given in the problem is linear, then you really can choose any two points on the graph, figure out their slope, and there’s your answer. A couple reminders:
*Make sure you are getting the units right. You want liters per kilometer, not kilometers per liter or something else. Here you are referring to x- and y-axes but it’s not immediately clear what those mean. I’m assuming f is a function of d, so it should be referred to as d- and f-axes respectively.
*You may want to choose (d,f) = (840,500) as one of your points, and choose another point as the second point (if it’s obviously on the line, then it’s a good candidate)
For example, if (d,f) = (1000,480) was another point, then the correct answer would be (500-480)/(1000-840) = 0.125 liters/km.