Question

30 POINTS! Explain how you found the equation that represents Aunt Andrea’s decorating plans from the table.

Answer 1

Answer:

The number of balloons varies directly with the number of tables. The two variables are directly proportional. The relationship of balloons to tables is the ratio 5:1, where 5 is the constant of variation. Use the equation y = kx, where k is the constant of variation resulting in the equation y = 5x.

Step-by-step explanation:

Answer 2

The equation for decorating plan from the table is an illustration of a linear equation.

The equation that represents the plan is: $y = 5x$

First, we calculate the slope (m) of the table using:

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

From the table (see attachment), we have:

$(x_1,y_1) = (3,15)$

$(x_2,y_2) = (4,20)$

So, the slope is:

$m = \frac{20 - 15}{4 - 3}$

$m = \frac{5}{1}$

$m = 5$

The equation is then calculated as:

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

This gives

$y = 5(x - 3) + 15$

$y = 5x - 15 + 15$

$y = 5x$

Hence, the equation that represents the plan is:

$y = 5x$

Read more about equations and tables at:

brainly.com/question/20106471