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Sveta_85 [38]
3 years ago
13

The table below represents a linear function in the equation represents a function. table numbers are X: -1,0,1. f(x): -3,0,3. G

(x): g(x) = 7x + 2
Part A: write a sentence to compare the slope of the two functions and show the steps used to determine the slope of FX and GX.

Part B: which function has a greater Y intercept? justify your answer
Mathematics
1 answer:
Alexxx [7]3 years ago
5 0
A)
SLOPE OF f(x)
To find the slope of f(x) we pick two points on the function and use the slope formula. Each point can be written (x, f(x) ) so we are given three points in the table. These are: (-1, -3) , (0,0) and (1,3). We can also refer to the points as (x,y). We call one of the points ( x_{1} , y_{1} ) and another ( x_{2} , y_{2} ). It doesn't matter which two points we use, we will always get the same slope. I suggest we use (0,0) as one of the points since zeros are easy to work with.

Let's pick as follows:
( x_{1} , y_{1} )= (0.0)
( x_{2} , y_{2} )= (1.3)

The slope formula is: m= \frac{y_{2} - y_{1} }{ x_{2}- x_{1}  }
We now substitute the values we got from the points to obtain.
m= \frac{3-0}{ 1-0 } = \frac{3}{1}=3

The slope of f(x) = 3

SLOPE OF g(x)
The equation of a line is y=mx+b where m is the slope and b is the y intercept. Since g(x) is given in this form, the number in front of the x is the slope and the number by itself is the y-intercept.

That is, since g(x)=7x+2 the slope is 7 and the y-intercept is 2.

The slope of g(x) = 2

B)
Y-INTERCEPT OF g(x)
From the work in part a we know the y-intercept of g(x) is 2.

Y-INTERCEPT OF f(x)
The y-intercept is the y-coordinate of the point where the line crosses the y-axis. This point will always have an x-coordinate of 0 which is why we need only identify the y-coordinate. Since you are given the point (0,0) which has an x-coordinate of 0 this must be the point where the line crosses the y-axis. Since the point also has a y-coordinate of 0, it's y-intercept is 0

So the function g(x) has the greater y-intercept
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Answer:

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Heather, Shen, and Aldo served a total of 57 orders Monday at the school cafeteria. Shen served 2 times as many as Aldo. Aldo se
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Answer:

Shen served 32 orders, Aldo served 16 orders and Heather served 9 orders

Step-by-step explanation:

Let S represent Shen, A, Aldo and H, Heather

Now, let's interpret the question

Shen served 2 times as many as Aldo, this gives:

S = 2A          ...eq 1

Aldo served 7 more orders than Heater

A = 7 + H     ... eq 2

Slot in the value of A in eq 1

Therefore,

S = 2 (7 + H)

Expand the bracket

S = 14 + 2H

Shen, Heather and Aldo served a total of 57 orders

S + A + H = 57

Slot in the values of S and A

(14 + 2H) + (7 + H) + H = 57

14 + 2H + 7 + H + H = 57

Collect like terms

14 + 7 + 2H + H + H = 57

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4H = 57 - 21

4H = 36

H = 9

Substitute the value of eq 2

A = 7 + H

A = 7 + 9

A = 16

Substitute the value of A in eq 1

S = 2A

S = 2(16)

S = 32

Therefore, Shen served 32 orders, Aldo served 16 orders and Heather served 9 orders

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