So i was going over a problem that i didn't understand which is What is the slope of the function described in the table below?

x I y
0 | -3
2 | -2
4 | -1
6 | 0
the choices were f) -3
g) 1/2
h) 2
J) 3
i know that the answer is g because my family told me but i don't understand why can someone please explain to me?

Look at the table.

x changes by +2
y changes by -1

The slope is the ratio of changes,

y-change / x-change = -1/2

So, the answer is g if there is a typo and it reads -1/2

ohhhhhhhh thank you so much but yeah i was wondering too because there was no negative signs but i think there was a typo

In your case x and y coordinates are:

x1 = 0, x2 = 2, x3 = 4, x4 = 6

y1 = - 3, y2 = - 2, y3 = -1, y4 = 0

slope = change in y / change in x

This mean, divide the change in height by the change in horizontal distance.

slope = ( y2 - y1 ) / ( x2 - x1 ) = [ - 2 - ( - 3 ) ] / ( 2 - 0 ) = ( - 2 + 3 ) / 2 = 1 / 2

slope = ( y3 - y2 ) / ( x3 - x2 ) = [ - 1 - ( - 2 ) ] / ( 4 - 2 ) = ( - 1 + 2 ) / 2 = 1 / 2

slope = ( y4 - y3 ) / ( x4 - x3 ) = [ 0 - ( - 1 ) ] / ( 6 - 4 ) = ( 0 + 1 ) / 2 = 1 / 2

Answer: g) 1 / 2 isn't a typo.

Damon has it right

What was I thinking???

Sorry, Bosnian.

Blew that, too.

To find the slope of a function, you need to calculate the change in the dependent variable (y) divided by the change in the independent variable (x). In this case, the independent variable (x) represents the values given in the table, and the dependent variable (y) represents the corresponding values.

Let's calculate the slope using two points from the table. We'll choose the points (0, -3) and (2, -2). The change in y is -2 - (-3) = 1, and the change in x is 2 - 0 = 2. Therefore, the slope between these two points is 1/2.

Now, let's choose another pair of points to double-check our answer. We'll use (2, -2) and (4, -1). The change in y is -1 - (-2) = 1, and the change in x is 4 - 2 = 2. Again, the slope between these two points is 1/2.

Since both calculations yield the same result, we can conclude that the slope of the function described in the table is indeed 1/2. Therefore, the correct answer is (g) 1/2.