Chapter 1.7, Problem 10IP

(a)

To determine

The equation that can be used to find the area of any 10 square floor tiles

Answer to Problem 10IP

The equation is $y=18x-72$

Explanation of Solution

Given information:

The pair of points, $\left(6,36\right),\text{and }\left(12,144\right)$

Concept Used:

Area of square

  $\text{area=side}\times \text{side}$

The slope of a line connecting the points $\left(x_1,y_1\right),\text{ and }\left(x_2,y_2\right)$ is given by the formula

  $\text{Slope }\left(m\right)=\frac{y_2-y_1}{x_2-x_1}$

  $\begin{array}{l}\text{Equation}\text{is}\\ \text{y}-{\text{y}}_1=m\left(x-x_1\right)\end{array}$

Calculation:

In order to find the slope of the line passing through the points $\left(6,36\right),\text{and }\left(12,144\right)$ , use the slope formula and substitute the values $\left(x_1,y_1\right)=\left(6,36\right),\text{and }\left(x_2,y_2\right)=\left(12,144\right)$ and simplify further as shown below,

  $\begin{array}{c}\text{Slope }\left(m\right)=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{144-36}{12-6}\\ =\frac{108}{6}\\ =18\\ \text{Equation}\text{is}\\ \text{y}-{\text{y}}_1=m\left(x-x_1\right)\\ y-36=18\left(x-6\right)\\ y-36=18x-108\\ y-36+36=18x-108+36\\ y=18x-72\end{array}$

Thus, the equation is $y=18x-72$

(b)

To determine

The table to find the area covered by 10 tiles

Answer to Problem 10IP

Side x	Area y
6	36
12	144
15	225
24	576

Explanation of Solution

Given:

Value of side of a square is 6,12,15 and 24.

Calculation:

In order to find the table we put the value of x in the area of square simplify as follow

  $\begin{array}{c}\text{area=side}\times \text{side}\\ {\text{area=x}}^2\\ \text{for x=6}\\ \text{area=6}\times \text{6}\\ \text{=36}\\ \text{for x=12}\\ \text{area=12}\times 12\\ =144\\ \text{for x=15}\\ \text{area=15}\times 15\\ =225\\ \text{for x=24}\\ \text{area=24}\times 24\\ =576\end{array}$

Thus, the table is given below

Side x	Area y
6	36
12	144
15	225
24	576

(c)

To determine

Graph of the ordered pair of the relation

Answer to Problem 10IP

  

Explanation of Solution

Given:

The point, $\left(6,36\right),\left(12,144\right),\left(15,225\right),\text{and}\left(24,576\right)$ .

Concept Used:

In rectangular coordinate system any poin be in the form of $\left(x,y\right)$ .

• In Quadrant I, both the coordinates of ordered pair are positive, that is, $\left(+,+\right)$ .
• In Quadrant II, first number is negative and second is positive, that is, $\left(-,+\right)$ .
• In Quadrant III, both the coordinates of ordered pair are negative, that is, $\left(-,-\right)$ .
• In Quadrant IV, first point is positive and second is negative, that is, $\left(+,-\right)$ .

In order to plot the point $\left(6,36\right),\left(12,144\right),\left(15,225\right),\text{and}\left(24,576\right)$ , observe that both numbers are same they are positive, so the point will be in first quadrant.

To plot the graph of the point $\left(6,36\right)$ , first move 6 units to the right starting from origin and then move 36 units up.

To plot the graph of the point $\left(12,144\right)$ , first move 12 units to the right starting from origin and then move 144 units up.

To plot the graph of the point $\left(15,225\right)$ , first move 15 units to the right starting from origin and then move 225 units up.

To plot the graph of the point $\left(24,576\right)$ , first move 24 units to the right starting from origin and then move 576 units up.

The graph of the point is shown below: