Math / Geometry

QuestionErnesto is creating a scale drawing of his bedroom. 1 inch in his drawing represents 12 inches in his bedroom.
Complete the table. \begin{tabular}{|l|c|c|c|c|} \hline 4) $)$ Bedroom (inches) & 12 & 24 & & \\ \hline 4 $)$ & Drawing (inches) & 1 & L & 5 \\ \hline \end{tabular}
Graph the data from the table.

Studdy Solution

STEP 1

What is this asking? We need to figure out how many inches in Ernesto's drawing represent 60 inches in his bedroom, and how many inches in his bedroom are represented by 2 inches in his drawing.
Then, we need to graph the relationship between the drawing measurements and the actual bedroom measurements. Watch out! It's easy to mix up the drawing measurements and the actual bedroom measurements, so let's stay focused!

STEP 2

1. Fill the table
2. Graph the data

STEP 3

Alright, let's decode this table!
We know that $1$ inch on the drawing equals $12$ inches in the real bedroom.
This is our golden rule!

STEP 4

The table shows that if the bedroom length is $24$ inches, the drawing length is $L$ inches.
Since $1$ inch in the drawing represents $12$ inches in the bedroom, we can set up a proportion: $\frac{1 \text{ inch (drawing)}}{12 \text{ inches (bedroom)}} = \frac{L \text{ inches (drawing)}}{24 \text{ inches (bedroom)}}$

STEP 5

To find $L$ , we can cross-multiply: $1 \cdot 24 = 12 \cdot L$ $24 = 12L$

STEP 6

Now, we want to isolate $L$ .
We can do this by dividing both sides of the equation by $12$ : $\frac{24}{12} = \frac{12L}{12}$ $2 = L$ So, $L = \mathbf{2}$ inches!
If the bedroom length is $24$ inches, the drawing length is $\mathbf{2}$ inches.
Makes sense, right?
Double the bedroom length, double the drawing length!

STEP 7

Now, let's tackle the next part of the table.
We know the drawing length is $5$ inches, but we need to find the corresponding bedroom length.
Let's call the unknown bedroom length $B$ .
Using our golden rule again, we set up another proportion: $\frac{1 \text{ inch (drawing)}}{12 \text{ inches (bedroom)}} = \frac{5 \text{ inches (drawing)}}{B \text{ inches (bedroom)}}$

STEP 8

Cross-multiplying gives us: $1 \cdot B = 12 \cdot 5$ $B = 60$ So, if the drawing length is $5$ inches, the bedroom length is $\mathbf{60}$ inches!

STEP 9

Let's visualize this!
We'll put the drawing measurements (in inches) on the horizontal axis (x-axis) and the bedroom measurements (in inches) on the vertical axis (y-axis).

STEP 10

From our table and calculations, we have the following points to plot: $(1, 12)$ , $(2, 24)$ , and $(5, 60)$ .
Remember, the first number in each pair is the drawing measurement, and the second number is the actual bedroom measurement.

STEP 11

Plot these points on your graph.
You should see that they form a straight line!
This is because the relationship between the drawing measurements and the bedroom measurements is linear.
For every $1$ inch increase in the drawing, there's a $12$ inch increase in the actual bedroom size.

STEP 12

The completed table is: \begin{tabular}{|l|c|c|c|c|} \hline Bedroom (inches) & 12 & 24 & 60 & \\ \hline Drawing (inches) & 1 & 2 & 5 \\ \hline \end{tabular} And the graph should show a straight line passing through the points $(1, 12)$ , $(2, 24)$ , and $(5, 60)$ .

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Studdy Solution

STEP 1

STEP 2

1. Fill the table
2. Graph the data

STEP 3

Alright, let's decode this table!
We know that $1$ inch on the drawing equals $12$ inches in the real bedroom.
This is our golden rule!

STEP 4

STEP 5

To find $L$ , we can cross-multiply: $1 \cdot 24 = 12 \cdot L$ $24 = 12L$

STEP 6

STEP 7

STEP 8

Cross-multiplying gives us: $1 \cdot B = 12 \cdot 5$ $B = 60$ So, if the drawing length is $5$ inches, the bedroom length is $\mathbf{60}$ inches!

STEP 9

Let's visualize this!
We'll put the drawing measurements (in inches) on the horizontal axis (x-axis) and the bedroom measurements (in inches) on the vertical axis (y-axis).

STEP 10

From our table and calculations, we have the following points to plot: $(1, 12)$ , $(2, 24)$ , and $(5, 60)$ .
Remember, the first number in each pair is the drawing measurement, and the second number is the actual bedroom measurement.

STEP 11

Plot these points on your graph.
You should see that they form a straight line!
This is because the relationship between the drawing measurements and the bedroom measurements is linear.
For every $1$ inch increase in the drawing, there's a $12$ inch increase in the actual bedroom size.

STEP 12

The completed table is: \begin{tabular}{|l|c|c|c|c|} \hline Bedroom (inches) & 12 & 24 & 60 & \\ \hline Drawing (inches) & 1 & 2 & 5 \\ \hline \end{tabular} And the graph should show a straight line passing through the points $(1, 12)$ , $(2, 24)$ , and $(5, 60)$ .

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Studdy Solution

STEP 1

STEP 2

1. Fill the table2. Graph the data

STEP 3

Alright, let's **decode** this table!We know that 111 inch on the drawing equals 121212 inches in the real bedroom.This is our **golden rule**!

STEP 4

STEP 5

To find LLL, we can **cross-multiply**: 1⋅24=12⋅L1 \cdot 24 = 12 \cdot L1⋅24=12⋅L 24=12L24 = 12L24=12L

STEP 6

STEP 7

STEP 8

**Cross-multiplying** gives us: 1⋅B=12⋅51 \cdot B = 12 \cdot 51⋅B=12⋅5 B=60B = 60B=60So, if the drawing length is 555 inches, the bedroom length is 60\mathbf{60}60 inches!

STEP 9

Let's **visualize** this!We'll put the drawing measurements (in inches) on the horizontal axis (x-axis) and the bedroom measurements (in inches) on the vertical axis (y-axis).

STEP 10

From our table and calculations, we have the following points to plot: (1,12)(1, 12)(1,12), (2,24)(2, 24)(2,24), and (5,60)(5, 60)(5,60).Remember, the first number in each pair is the drawing measurement, and the second number is the actual bedroom measurement.

STEP 11

Plot these points on your graph.You should see that they form a straight line!This is because the relationship between the drawing measurements and the bedroom measurements is **linear**.For every 111 inch increase in the drawing, there's a 121212 inch increase in the actual bedroom size.

STEP 12

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1. Fill the table
2. Graph the data

Alright, let's decode this table!
We know that $1$ inch on the drawing equals $12$ inches in the real bedroom.
This is our golden rule!

To find $L$ , we can cross-multiply: $1 \cdot 24 = 12 \cdot L$ $24 = 12L$

Cross-multiplying gives us: $1 \cdot B = 12 \cdot 5$ $B = 60$ So, if the drawing length is $5$ inches, the bedroom length is $\mathbf{60}$ inches!

Let's visualize this!
We'll put the drawing measurements (in inches) on the horizontal axis (x-axis) and the bedroom measurements (in inches) on the vertical axis (y-axis).

From our table and calculations, we have the following points to plot: $(1, 12)$ , $(2, 24)$ , and $(5, 60)$ .
Remember, the first number in each pair is the drawing measurement, and the second number is the actual bedroom measurement.

Plot these points on your graph.
You should see that they form a straight line!
This is because the relationship between the drawing measurements and the bedroom measurements is linear.
For every $1$ inch increase in the drawing, there's a $12$ inch increase in the actual bedroom size.