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

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)

The table below represents a linear function f(x) and the equation represents a function-example-1

1 Answer

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Answer:

Slope of f(x) is greater than slope of g(x)

g(x) has a greater y intercept

Explanation:

Given

f(x) table


g(x) = 2x + 6

Solving (a):

First, we determine the slope of f(x).

From the table, we take any two corresponding values of x and f(x).

Represent f(x) with y


(x_1,y_1) = (-1.-12)


(x_2,y_2) = (0.-6)

The slope (m) is calculated as thus


m = (y_2 - y_1)/(x_2 - x_1)


m = (-6 - (-12))/(0 - (-1))


m = (-6 +12)/(0 +1)


m = (6)/(1)


m = 6

Represent this with m1


m_1 = 6

Calculating the slope of g(x).

The general form of an equation is
y = mx + b

Where m represents the slope.

We have that:


g(x) = 2x + 6

By comparing
g(x) = 2x + 6 with
y = mx + b


m = 2

Represent this with m2


m_2 = 2

Comparing both slope, we can say that:

f(x) has a greater than slope of g(x)

Another comparison is that:

Slope of f(x) is 3 times the slope of g(x)

Solving (b): Function with greater y intercept.

The general form of an equation is
y = mx + b

Where b represents the y intercept.

First, we need to determine the equation of f(x) using:


y - y_1 = m(x - x_1)

Recall that, from the table of f(x):


(x_1,y_1) = (-1.-12)


(x_2,y_2) = (0.-6)


m_1 = 6

So:


y - y_1 = m(x - x_1)


y - (-12) = 6(x - (-1))


y + 12 = 6(x +1)


y + 12 = 6x +6

Solve for y


y = 6x + 6 - 12


y = 6x - 6

By comparing this with
y = mx + b, the y intercept of f(x) is -6

For g(x), we have:


g(x) = 2x + 6

By comparing this with
y = mx + b, the y intercept of g(x) is 6

Comparing the y intercepts of both functions, g(x) has a greater y intercept because
6 > -6

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