Question

To write the equation of a line that passes through points (1,1) and (3,5), answer the following questions to guide your thought process:

A) Given points (x_{1}, y_{1}) and (x_{2}, y_{2}) what is the equation for slope?

m =

5

Y_{2}

x_{1}

y_{1}

x_{2}

B) What is the slope of a linear function containing the points (1, 1) and (3,5)?

m =
Top part
5

1

Bottom part

3

1

m =

*blank 1*

*blank 2*

m=

*blank 3*

Options for blanks 1 and 2

A 2
B -2
C 4
D -4

Options for blank 3

A -1/2
B 2
C -2
D 1/2

Answer 1

To solve the problem step-by-step, let's start with the questions provided:

### A) Given points \( (x_{1}, y_{1}) \) and \( (x_{2}, y_{2}) \), what is the equation for slope?

The formula for calculating the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

### B) What is the slope of a linear function containing the points (1, 1) and (3, 5)?

1. Identify the coordinates of the points:
- \( (x_1, y_1) = (1, 1) \)
- \( (x_2, y_2) = (3, 5) \)

2. Substitute into the slope formula:
\[
m = \frac{5 - 1}{3 - 1}
\]
- The top part (numerator) is \( 5 - 1 = 4 \) (which corresponds to blank 1)
- The bottom part (denominator) is \( 3 - 1 = 2 \) (which corresponds to blank 2)

Thus:
- **Blank 1 = 4**
- **Blank 2 = 2**

Now we can calculate \( m \):
\[
m = \frac{4}{2}
\]
\[
m = 2
\]
This corresponds to **Blank 3 = 2**.

So, the filled blanks are:
- **Blank 1: 4**
- **Blank 2: 2**
- **Blank 3: 2**

### Final Answer:
- Blank 1: **4**
- Blank 2: **2**
- Blank 3: **2**