Question

Explain how to write a function rule from the table below. Then write a function rule. x 2 4 6 y 1 0 -1

Answer 1

okay so basically whats the difference in the first column

Answer 2

x your adding by two, and y your subtracting by 1.

Answer 3

http://www.youtube.com/watch?v=I6Dxybru8NY
hold im im watching this .-. i havent done this stuff since like 8th grade. what are you in anyways?

Answer 4

Okay its fine. 8th grade.

Answer 5

that explains it. @Hero
if it were y problem i would put x+2=y-1 but that dosent look right so ill have hero do it! ^.^

Answer 6

Okay :) Thank you for the help. :)

Answer 7

It's a linear function, so start by taking any two points and finding the slope of the line.

Answer 8

Okay.

Answer 9

I still cant really figure this out.

Answer 10

Have you ever been shown how to find the slope of a line given two points before?

Answer 11

I dont think so.

Answer 12

Im not really good at math. :/

Answer 13

In general, if you are given two points \((x_1, y_1)\) and \((x_2, y_2)\), then you plug those points in to the formula below, to find the slope, \(m\):

\(m = \dfrac{y_2 - y_1}{x_2 - x_1}\)

Answer 14

For example, suppose you were given two points \((2 , 4)\) and \((3,6)\) and asked to find the slope of the line that contains both points. Using the slope formula, you would insert the coordinates of each point in to the formula to get:

\(m = \dfrac{6 - 4}{3 - 2} = \dfrac{2}{1} = 2\)

Which means the slope of the line containing the given points is 2.

Answer 15

Ohhh okay.

Answer 16

Now suppose you wanted to find the equation of the line. If you wanted to do that, you would need to know the formula for the equation of a line. The formula for equation of a line is

y = mx + b with the following conditions:

(x,y) is any point on the line
m is the slope of the line
b is the y-intercept or the point where the line crosses the y-axis.

Answer 17

In this case, we have two points and the slope, but we only need to use one of the points along with the slope, and then find the value of b. We will use the point (2,4) and the slope m = 2 and insert those values in to the equation of the line formula. Once we do that we'll have:

4 = 2(2) + b

Then solving for b, we'll get:

4 = 4 + b
4 - 4 = b
0 = b

Now, we must write the equation of the line in slope-intercept form, meaning, we will include the value of the slope and the value of the y-intercept in the equation of the line:

The equation of the line is y = mx + b. After inserting m = 2 and 0 = b, we have

y = 2x

Answer 18

https://www.desmos.com/calculator/jbj20gzvag

Answer 19

The graph of y = 2x along with the plot of the points confirms that both given points are indeed on the equation of the line we found.

Answer 20

To write y = 2x as a linear function, we simply replace y with f(x) to get

f(x) = 2x

Answer 21

The information I provided you with is only an example of how to find the slope of a line, the equation of a line, and how to write the equation of a line as a linear function. However, it is not the solution to the problem you presented.

Answer 22

Okay thank you so much Hero!!