Q9. - Algebra 1

Question

The data in the table show the size of a room in square feet and the time it takes to paint the room in minutes.

Room Size	100	150	200	400	500
Painting time	160	230	270	500	680

1. Use the points $\left(100,160\right)$ and $\left(500,680\right)$ to write an equation in slope-intercept form.
2. Predict the amount of time required to paint a room measuring 750 square feet.

Step-by-Step Solution

Answer

a. The required equation is represented by $y=\frac{13}{10}x+30$.  

 

b. The required time in minutes is represented by 1005.  

Part a. Step 1. Determine the formula that can be used.

The standard form associated with line that is having a travel through points which are two in count $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$ can be used to calculate the required equation.

Part a. Step 2. Take the help of the obtained method.

Take the help of obtained standard form represented by $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$ in which the required values can be filled by using the provided points as they are in the form of $\left(x_1,y_1\right)$$\left(x_2,y_2\right)$.

$$\begin{gathered} y-160=\frac{680-160}{500-100}\left(x-100\right) \\ y-160=\frac{13}{10}\left(x-100\right) \\ y=\frac{13}{10}\left(x\right)-130+160 \\ y=\frac{13}{10}x+30 \end{gathered}$$

Part a. Step 3. Write the conclusion.

The obtained equation is $y=\frac{13}{10}x+30$ so it is the required equation.

Part b. Step 1. Determine the method that can be used.

The equation obtained in first part of the question can be used that is $y=\frac{13}{10}x+30$.

Part b. Step 2. Take the help of the obtained method.

Take the help of obtained method and substitute 750 in place of x into it and perform simplification.

$$\begin{gathered} y=\frac{13}{10}\times 750+30 \\ y=1005 \end{gathered}$$

Part b. Step 3. Write the conclusion.

The obtained value is 1005 that represents the time in minutes.