Question

Consider the linear function y = 5x + 12 and the linear function represented by the table of values below.

Answer 1

Answer:

(a) and (f)

Step-by-step explanation:

Given

$y = 5x + 12$

See attachment for table and options

First, we calculate the slope of the table

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

Using:

$(x_1,y_1) = (2,29)$

$(x_1,y_1) = (4,53)$

So, we have:

$m = \frac{53- 29}{4 - 2}$

$m = \frac{24}{2}$

$m = 12$

The equation is then calculated using:

$y = m(x -x_1) + y_1$

This gives:

$y = 12*(x -2) + 29$

$y = 12x -24 + 29$

$y = 12x+5$

So, we have:

$y = 5x + 12$ --- The given equation

and

$y = 12x+5$ --- The equation of the table

An equation is represented as:

$y = mx + b$

Where:

m = slope or rate of change

b = y intercept

So, for the given equation: $y = 5x + 12$

Rate of change = 5

y intercept = 12

For the table: $y = 12x+5$

Rate of change = 12

y intercept = 5

In conclusion:

(a) $y = 12x+5$ has the greater rate of change:

and

(f) $y = 5x + 12$ has the greater y intercept