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Alex777 [14]
3 years ago
5

The table below represents a linear function f(x) and the equation represents a function g(x): x f(x) −1 −7 0 −1 1 5 g(x) g(x) =

5x − 4 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)
Mathematics
1 answer:
astra-53 [7]3 years ago
8 0
Question A:

Rewriting the table for f(x):

x      -1       0      1
f(x)   -7      -1      5

Notice that for every increase of one unit in 'x', there are an increase 6 units on f(x). Hence, the gradient of the slope of f(x) is 6. 

g(x) = 5x - 4 ⇒ This function follows the general form of the straight line equation, y = mx + c, where 'm' is the gradient and 'c' is the y-intercept.
Hence, the gradient of the slope of g(x) is 5.

The slope of f(x) is steeper than the slope of g(x).

---------------------------------------------------------------------------------------------------------------

Question B:

The y-intercept is the value of y where a straight line crosses the y-axis (or when x is zero).

From the table of f(x), the y-intercept is -1 (this is the value of 'y' when 'x' is zero)

From the given function g(x) = 5x - 4, the y-intercept is -4. 

f(x) has a greater y-intercept.



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7 0
3 years ago
Find the number which when divided by 4 and increased by 12 is the same as when it is divided by 3 and decreased by 5
MatroZZZ [7]

Step-by-step explanation:

Let's make the number we're finding to be a. So, it says that it will be divided by 4 and then added by 12 if we want this in algebraic expression it will be \frac{a}{4} +12\\. It's also telling us that that expression is the same thing as our number divided by 3 and subtracted by 5. If we want an expression out of it it well be \frac{a}{3} -5\\. Since they are the same, we have the equation below.

\frac{a}{4} +12 = \frac{a}{3} -5\\

All we have to do now is to find a.

\frac{a}{4} +12 = \frac{a}{3} -5 \\ \frac{a +48}{4} = \frac{a -15}{3} \\ (3)(a +48) = (a - 15)(4) \\ 3a +144 = 4a -60 \\ (60 -3a) + 3a +144 = 4a -60 +(60 -3a) \\ a = 204

<h3>Answer:</h3>

Our number must be 204. I think

5 0
3 years ago
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