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Amiraneli [1.4K]
3 years ago
13

Don’t really know what linear functions are

Mathematics
1 answer:
kondaur [170]3 years ago
3 0

Answer:

The rate of change of f(x) is greater than that of g(x)

They have the same y intercept of 14

Step-by-step explanation:

Given

g(x) = -\frac{1}{2}x + 14

Table for function f(x)

Required

Compare their rate of change and intercept

For g(x), we have:

g(x) = -\frac{1}{2}x + 14

The form of an equation is:

y = mx + b

Where

m = slope

b =y\ intercept

So:

m = -\frac{1}{4}

b = 14

For f(x): Start by calculating the slope (m)

m = \frac{y_2 - y_1}{x_2 - x_1}

m = \frac{17-16}{6-4}

m = \frac{1}{2}

The intercept is calculated using:

m = \frac{y_2 - y_1}{x_2 - x_1}

Where

(x_1,y_1) = (-2,13)

(x_2,y_2) = (0,y) --- we want to solve for y

So:

\frac{1}{2} = \frac{y - 13}{0 --2}

\frac{1}{2} = \frac{y - 13}{2}

Multiply both sides by 2

1 =y - 13

Make y the subject

y =1 + 13

y = 14

So, we have:

m = -\frac{1}{4} and b = 14 -- for g(x)

m = \frac{1}{2} and y = 14 --- for f(x)

By comparison:

The rate of change (i.e. slope) of f(x) is greater than that of g(x) because 1/2 > -1/2

They have the same y intercept of 14

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