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 =

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

*blank 1*

*blank 2*

Bottom part

*blank 3*

*blank 4*


Options for all blanks
A 1
B 3
C 5

Answer 1

A) The equation for the slope \( m \) of a line that passes through two points \((x_{1}, y_{1})\) and \((x_{2}, y_{2})\) is given by:

\[
m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}
\]

B) To find the slope of a linear function containing the points (1, 1) and (3, 5):

Using the points:
- \( (x_{1}, y_{1}) = (1, 1) \)
- \( (x_{2}, y_{2}) = (3, 5) \)

Substituting into the slope formula:
\[
m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{5 - 1}{3 - 1}
\]

Top part:
- *blank 1* = 5 (which is \( y_{2} \))
- *blank 2* = 1 (which is \( y_{1} \))

Bottom part:
- *blank 3* = 3 (which is \( x_{2} \))
- *blank 4* = 1 (which is \( x_{1} \))

Thus, the slope \( m \) is calculated as follows:

\[
m = \frac{5 - 1}{3 - 1} = \frac{4}{2} = 2
\]

Therefore, the answers for the blanks are:
- *blank 1* = 5
- *blank 2* = 1
- *blank 3* = 3
- *blank 4* = 1

So the slope \( m \) is equal to 2.