Question

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

x f(x)
-1 -11
0 -1
1 9

g(x)
g(x)=5x+1

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).

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

Answer 1

linear function : (just so u know, f(x) is y)

slope formula : (y2 - y1) / (x2 - x1)
(-1,-11)(0,-1)
slope = (-1 - (-11) / (0 - (-1) = (-1 + 11) / (0 + 1) = 10/1 = 10

now we take y - mx + b
slope(m) = 10
(0.-1)...x = 0 and y = -1
now we sub, we r looking for b, the y int
-1 = 10(0) + b
-1 = b
so the equation of the line is : y = 10x - 1...so the slope is 10 and the y int is -1

function : g(x) = 5x + 1
y = 5x + 1
y = mx + b.....In this form, the m is ur slope and the b is ur y int...so the slope is 5 and the y int is 1

The linear function f(x) has a slope of 10 compared to the g(x) function, which has a slope of 5
g(x) = 5x + 1 has the greater y int.

Answer 2

Explanation:

We have two functions and as per the required options

We have point in f(x) as (x,f(x))=(0,-1) and (1,9)

We will find the slope which is:

`(y_2-y_1)/(x_2-x_1)`

`y_2=9,y_1=-1,x_2=1,x_1=0`

`(9-(-1))/(1-0)`

`(10)/(1)=10`

And slope of g(x) will be calculated by the general equation of the line

y =mx+c

where m is slope

So, the slope of g(x)=5x+1

m=5

Slope of f(x)=10

and slope of g(x)=5

Slope of f(x) is greater than that of g(x).

Part B:

y-intercept is the point where x=0

So, y-intercept of g(x) will be calculated by substituting x=0

g(0)=5(0)+1=1

Hence, y-intercept of g(x) is 1.

And for y-intercept of f(x) we will use the point (0,-1)

Equation will become

f(x)=mx+c

`f(x)=m(0)+(-1)`

Here, when x is 0 y=-1

hence, y-intercept of f(x) is -1

Function g(x) has greater y-intercept.