ASAP PLEASE I NEED TO SOLVE THIS

Question

Find the equation for the linear function that passes through the points (3, 2) and (6, 10).

Round all answers to 4 decimal places as needed

___________

Find the equation for the exponential function that passes through the points (3, 2) and (6, 10).

Round all answers to 4 decimal places as needed

___________

Answer 1

To find the equation of a linear equation given two points you need to first use the coordinates to find the slope of the line, and then use the pouint slope formulat to get the equation.

First, let's get the slope. That would be the change of y divided by the change of x, or the rise divided by the run. We have two points to work with, (3,2) and ((6,10), which are (x1, y1) and (x2, y2). Subtratct y1 from y2 to get the change of y, or the rise:

10 - 2 = 8

Then subtract x1 from x2 to get the change of x, or the run:

6 - 3 = 3

Now divide the change of y by the change of x:

8/3 = slope

Now we can choose either of the points to plug into the point/slope formule,

(y - y1) = m(x - x1), remember that m is equal to the slope of the line, so let's use the point (3,2)

(y - 2) = 8/3(x - 3), distribute the 8/3 across (x - 3)

(y - 2) = (8/3)x - 8, add 2 to both sides

y = (8/3)x -6, or y = 8x/3 - 6

For the second question, we will use the relationship that for an exponential function y = ab^x, and then plug in the x and y values from the two data points. Let's work that out:

For (3,2), we get

2 = ab³

And for (6,10) we get

10 = ab⁶

Now divide the second equation by the first one, and we have:

(10 = ab⁶ )/(2 = ab³ ) = (5 = b³)

So b = 5^1/3

Now substitute that value for b into either equation to get a

The first equation will be easier because (b³)^1/3 = b, so we get

2 = ab³ , plug in 5^1/3 for b, so that is

2 = a (5^1/3)³ = 5a, so a = 2/5

Now we have a and b, so plug those into y = a(b^x), and we get

y = 2/5(5^1/3)^x , and then simplifying using the multiplication rule of exponents, we get

y = 2/5(5^x/3)

Hope this helps

Answer 2

Use the two-point form of a linear equation:

(y - 2) / (x - 3) = (2 - 10) / (3 - 6)

Can you simplify and answer?