Question

Use the given cost table for the same product from two different companies to create a linear system.

Answer 1

The true statements are:

• The linear equation for iSpace and Space Magic are $y=11.75x +4$ and $y=10.25x+16$ respectively
• Both iSpice and Spice Magic charge $98 for 8 pounds of paprika.

What is a linear function?

The question is an illustration of a linear function; a linear function is a function that has a constant rate/slope

A linear function is represented as:

$y=mx + c$

Where

• m represents slope
• c represents the y-intercept

Linear Equation of iSpice

Start by calculating the slope using:

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

So, we have:

$m = \frac{51 - 15.75}{4 -1}$

$m = 11.75$

The linear equation is then calculated as:

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

So, we have:

$y=11.75(x -1) + 15.75$

$y=11.75x -11.75 + 15.75$

$y=11.75x +4$

Linear Equation of Spice Magic

Start by calculating the slope using:

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

So, we have:

$m = \frac{57 - 26.25}{4 -1}$

$m = 10.25$

The linear equation is then calculated as:

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

So, we have:

$y=10.25(x -1) + 26.25$

$y=10.25x -10.25 + 26.25$

$y=10.25x+16$

The price, when both costs are the same

To do this, we simply equate both equations

$11.75x +4 = 10.25x + 16$

Collect like terms

$11.75x -10.25x = -4+ 16$

$1.5x = 12$

Solve for x

$x = 8$

Substitute 8 for x in any of the equations.

$y=11.75 \times 8 +4$

$y=98$

Hence, the price of both products will be the same at $98.00

Read more about linear equations at:

brainly.com/question/26227508