I'm a little confused on how to solve this:
The number of cricket chirps per minute is given by
N(t) = 7.2t - 32
Where t is the temperature in degrees Celsius.
a. Graph the equation N(t) = 7.2t - 32
I have learned a few ways to graph equations. One way would be to use -32 as the y-intercept and from there go up 7.2, over 1, etc. The other way would be to pick an x, or in this case, t value, multiply it by 7.2, subtract 32, and that would be the y value. I have tried both ways and gotten different results, so which way would be correct?
Thank you very much! Any help is appreciated!
both ways are correct, you must have made an error
method 1 - slope y-intercept
one point is obviously (0,-32)
now from there go up 7.2 then to the right 1
this would give you (1,-24.8)
join these two points
method 2: finding random ordered pairs
let t = 1, N(1) = 7.2-32 = -24.8 -- (1,-24.8)
let t = 3 N(3) = -10.4 --- (3,-10.4)
join these points, bet you get the same line
Thank you so much!
To graph the equation N(t) = 7.2t - 32, there are actually multiple ways you can approach it. Both methods you mentioned can be used, but they may yield different results due to errors or inaccuracies in plotting the points.
Here's a step-by-step explanation of both methods:
Method 1: Using the y-intercept and slope
1. Start by plotting the y-intercept, which is -32. This is the value of N(t) when t = 0.
2. Determine the slope, which is 7.2. This represents how much N(t) changes for every unit change in t.
3. Using the slope, you can plot additional points by finding the change in N(t) when the change in t is 1. For example, if you increase t by 1, N(t) will increase by 7.2. Plot a point at t = 1 and N(t) = -32 + 7.2.
4. Repeat step 3 multiple times to plot additional points.
5. Once you have a few points, connect them with a straight line to form the graph of the equation N(t) = 7.2t - 32.
Method 2: Evaluating N(t) for specific t-values
1. Choose different t-values, for example, -10, 0, 10.
2. Plug in each t-value into the equation N(t) = 7.2t - 32 to find the corresponding N(t) value.
3. Plot the points representing the t-values and their corresponding N(t) values on a graph.
4. Connect the points with a straight line to form the graph of N(t) = 7.2t - 32.
Both methods should yield the same graph if done correctly. If you're getting different results, double-check your calculations and ensure you're accurately plotting the points on the graph.