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Function A and Function B are linear functions. Function A x y – 10 – 14 – 1 – 5 9 5 Function B y=2x+4 Which statement is true?

Sagot :

MrRoyal

Answer:

See explanation

Step-by-step explanation:

Function A is not clear; I will use the following in place of function A

Function A:

[tex]x \to\ 1 |\ 3 |\ 4 |\ 6[/tex]

[tex]y \to -1|\ 3|\ 5|\ 9[/tex]

Function B:

[tex]y = 2x + 4[/tex]

Required

Compare both functions

For linear functions, we often compare the slope and the y intercepts only.

Calculating the slope of function A, we have:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Where:

[tex](x_1,y_1) = (1,-1)[/tex]

[tex](x_2,y_2) = (3,3)[/tex]

So, we have:

[tex]m = \frac{3 - -1}{3 - 1}[/tex]

[tex]m = \frac{4}{2}[/tex]

[tex]m = 2[/tex]

To calculate the y intercept, we set [tex]x = 0[/tex], then solve for y

i.e.[tex](x,y) = (0,y)[/tex]

Using the slope formula, we have:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Where:

[tex]m = 2[/tex]

[tex](x_1,y_1) = (0,y)[/tex]

[tex](x_2,y_2) = (3,3)[/tex]

So, we have:

[tex]2 = \frac{3 - y}{3 - 0}[/tex]

[tex]2 = \frac{3 - y}{3}[/tex]

Multiply by 3

[tex]6 = 3 - y[/tex]

Collect like terms

[tex]y = 3 - 6[/tex]

[tex]y = -3[/tex]

So, for function A:

[tex]m = 2[/tex] -- slope

[tex]y = -3[/tex] --- y intercept

For function B

[tex]y = 2x + 4[/tex]

A linear function is represented as:

[tex]y = mx + b[/tex]

By comparison

[tex]m = 2[/tex] --- slope

[tex]b = 4[/tex] --- y intercept

By comparing the results of both functions, we have the following conclusion:

Functions A and B have the same slope (i.e. 2)

Function B has a greater y intercept (i.e. 4)

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