Question

The table below represents a linear function f(x) and the equation represents a function g(x):


x f(x)
−1 −9
0 −1
1 7
g(x)

g(x) = 3x − 2


Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x). (6 points)

Part B: Which function has a greater y-intercept? Justify your answer. (4 points)

Answer 1

To get the slope from your table of values, you have to use the slope formula and two coordinate points at a time. Because they tell you that the function is linear, that means that the slope will be the same between any two points you pick so you only need to use two points to determine the slope. The formula is \[\frac{ y2-y1 }{ x2-x1 }\]

Answer 2

in your case the formula would be filled in as such:
\[\frac{ -9- (-1)}{ -1-0 }\]
\[\frac{ -9+1 }{ -1 }\] \[\frac{ -8 }{ -1 }\] =8

Answer 3

So the slope from your table is 8.

Answer 4

From the equation g(x) they gave you, in the form y = mx + b, the "m" is your slope. That m has a value of 3. That's part A. For part B, you have to write an equation for the values from your table in order to find the y intercept. Using the slope you found of 8 and one of the points from your table, you will use the point-slope form of an equation to write the equation. Let's use the point (1,7) because there are no negatives in it. Ok? I doesn't matter which ordered pair you choose, the equation will come out the same no matter which point you pick.

Answer 5

\[y-y_{1}=m(x-x_{1})\]

Answer 6

oh ok which part does each of them go in ?

Answer 7

Filling in your values for x1 and y1 using the point (1,7), your equation is
y−7=8(x−1)

Answer 8

let me finnish ok

Answer 9

Doing the math on that gives you an equation of y = 8x-1. This is now in slope-intercept form, with the m as your slope of 8 and the b is your y intercept. Here, your intercept is -1. From the g(x) equation they gave you, your y intercept is -2. Now let's answer the question in part B.

Answer 10

The y intercept from the table is -1 and the y intercept from your g(x) equation is -2, so the greater intercept is -1 (cuz -1 is bigger than -2). And that's it!