which function has the largest slope?
1)
x f(x)
-3 -10
-1 -7
1 -4

2)
g(x) equals one-half x plus 3

3) Lance gains 1 level each time he plays his favorite video game. He started at level 10

Question

which function has the largest slope? 
1)
x f(x) 
-3 -10 
-1 -7 
1 -4 

2) 
g(x) equals one-half x plus 3 



3) Lance gains 1 level each time he plays his favorite video game. He started at level 10

mathstudent55 · Answer

For 1), you have 3 points of the function.
Use any two points and find the slope.

For points $(x_1, y_1) $ and $(x_2, y_2) $, the slope is

$slope = m = \dfrac{y_2 - y_1}{x_2 - x_1} $

anonymous · Answer

i dont know how to do any of this /:

mathstudent55 · Answer

What do you get for the slope in 1)?

mathstudent55 · Answer

Ok. For part 1), let's choose the points (-3, -10) and (1, -4).
Each point has an x-coordinate followed by a y-coordinate like this: (x, y)

mathstudent55 · Answer

To find the slope, find the difference of the y-coordinates and divide by the difference of the x-coordinates.

mathstudent55 · Answer

For those two points, what are the y-coordinates?

anonymous · Answer

2/-3 ?

mathstudent55 · Answer

The y-coordinates are -10 and -4
The x-coordinates are -3, 1
Subtract the y-coordinates and divide by the subtraction of the x-coordinates to get the slope.

$slope = m = \dfrac{-10 - (-4)}{-3 - 1} = \dfrac{-6}{-4} = \dfrac{3}{2} $

vera_ewing · Answer

Great explanation @mathstudent55 ! It's very helpful! :)

mathstudent55 · Answer

Now we need to find the slope for part 2).

mathstudent55 · Answer

In part 2) we have an equation: 

$g(x) = \dfrac{1}{2}x + 3$

This is the equartion of a line is slope-intercept form, $y = mx + b$m, where m = slope.

We can read the slope directly. It is the number that multiplies x.

For part 2_, the slope is $\dfrac{1}{2} $.

anonymous · Answer

thank you so much

mathstudent55 · Answer

Now we need to deal with part 3).
Lance started at Level 10, so we start with 

y = 10

For each time, x, he plays, he gains 1 level, y.
That means as x goes up 1, y goes up 1, and so on. 

We simply add x to 10, or

$y = x + 10$

Since this is also in slope-intercept form, we again read off the slope directly. Since x = 1x, the slope is 1.

mathstudent55 · Answer

Now we have the 3 slopes, and you can decide which one is largest.

anonymous · Answer

so the first one is largest right?

anonymous · Answer

thank you!!

mathstudent55 · Answer

Correct. Between 3/2, 1/2 and 1, 3/2 is largest.

mathstudent55 · Answer

You're welcome.

anonymous · Answer

you were  alot of help thanks so much

mathstudent55 · Answer

You're welcome,