Question

Consider the linear function that is represented by the equation y=4x+5 and the linear function that is represented by the table below.
x y

2 16

4 26

6 36

8 46

Which statement is correct regarding their slopes and y-intercepts?



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Answer 1

Answer:

The slope and y-intercept of the table are greater than the slope and y-intercept of the equation.

Step-by-step explanation:

The slope of y = 4x + 5 is 4 and the y-intercept is (0,5).

The slope of the table is found by subtracting two points from the table in the formula $m=\frac{y_2-y_1}{x_2-x_1}$.

$m=\frac{26-16}{4-2}=\frac{10}{2}=5$

This means that the function increases by 5 for every x value that increases by 1. Knowing this, you can work backwards by subtracting 5 to find when x=0 (the y-intercept). When x=1 then y= 11. When x =0 then x =6. The table has the y-intercept (0, 6)

The slope and y-intercept of the table are greater than the slope and y-intercept of the equation.

This is true since 5 > 4 and 6>5.

Answer 2

Answer:

D) The function that is represented by the table has a steeper slope and a greater y-intercept.

Step-by-step explanation:

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