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kirill [66]
3 years ago
10

The rule for Function A is y= -2/3x

Mathematics
1 answer:
Rom4ik [11]3 years ago
6 0

Answer:

Both functions have negative rates of change

Function B has a greater rate of change than Function A

Step-by-step explanation:

we know that

<em>Function A</em>

The rule for Function A is

y=-\frac{2}{3}x

This is the equation of a proportional relationship (the line passes through the origin)

The slope is equal to m=-\frac{2}{3}

<em>Function B</em>

Find the equation of the function B

we have the points (-2,0) and (0,-2)

<em>Find the slope</em>

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

substitute the values

m=\frac{-2-0}{0+2}

m=\frac{-2}{2}

m=-1

The equation of the function B in slope intercept form is equal to

y=mx+b

we have

m=-1\\b=-2

substitute

y=-x-2

<u><em>Verify each statement</em></u>

Option 1) Both functions have negative rates of change

The statement is true

Because, the rate of change is the slope of the linear equation

Function A ----> m=-\frac{2}{3}

Function B ----> m=-1

Option 2) Both functions have the same rate of change.

The statement is false (see the explanation)

The rate of change are different ( m=-2/3 and m=-1)

Option 3) When graphed, Function A and Function B are parallel

The statement is false

When graphed, Function A and Function B are intersecting lines, because their slopes are different

Option 4) Function B has a greater rate of change than Function A

The statement is true

Remember that the rate of change can be either positive (increasing function) or negative (decreasing function). To find out which function has a greater rate of change, compare the absolute value of their slopes

therefore

1 > 2/3

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Step-by-step explanation:

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For k = 3,

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For k = 4,

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A system of equations is shown below.
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Given:

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The true statement about the given system of equations.

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We have,

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On comparing these two lines with slope intercept form, we get

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