we have the equation
y-2=4(x-7)
Convert to slope-intercept form
y=mx+b
Isolate the variable y
y-2=4x-28
y=4x-28+2
y=4x-26 -------> equation in slope-intercept form
Convert to function notation
<h2>f(x)=4x-26</h2>
Does the question have a photo attached on your screen because it sounds like the image you included is not completed
Answer:
3 and 9
if f(x)=x^2+13 and g(x)=12x-14
Step-by-step explanation:
So when we are looking for the intersection of two functions, we are trying to figure out when they are the same. When you think same, you should think equal (=).
So we want to find when f(x)=g(x) for x.
f(x)=g(x)
Let's get everything to one side.
Subtracting 12x and adding 14 to both sides.
I'm going to reorder the left hand side and also simplify the 13+14 part:
Now since the coefficent of x^2 is just 1 our job is to find two numbers that multiply to be 27 and add up to be -12.
Those numbers are -3 and -9 since -3(-9)=27 and -3+(-9)=-12.
So the factored form of our equation is
Since the product is 0, then at least one of the factors must be 0.
So we want to solve both x-3=0 and x-9=0.
x-3=0 can be solved by adding 3 on both sides. This gives us x=3.
x-9=9 can be solved by adding 9 on both sides. This gives us x=9.
The intersection of f and g happens at x=3 or x=9.
If you have learned how to find the line of best fit manually, then you can do it that way. Perhaps you may want to just find a line that can connect at least two of the points and I believe that that line will be able to represent the other points because, in general, the points are pretty close to one another.
If you don't want to do it manually and have a graphing calculator (which I recommend) then you can use that to find the line of best fit (and if you want then you can see how precise your points are with your r^2 value). Or there is a website (http://illuminations.nctm.org/Activity.aspx?id=4186), which you can use to help you to find the equation of that particular line.
Once you have that done, then you can substitute 2009 for the x value in the equation and then see what y value the equation produces. That will then be your answer :)
Since 4>1, this represents exponential growth.
