Question

Find the slope of the line passing through the points given below or state that the slope is undefined. Then indicate whether the line through the points​ rises, falls, is​ horizontal, or is vertical.
left parenthesis 5 comma 2 right parenthesis and left parenthesis 6 comma 4 right parenthesis
Question content area bottom
Part 1
Select the correct choice below​ and, if​ necessary, fill in the answer box within your choice.
A.
The slope is
  
enter your response here.
B.
The slope is undefined.
Part 2
Indicate whether the line through the points​ rises, falls, is​ horizontal, or is vertical. Choose the correct answer below.
A.
The line is vertical.
B.
The line rises from left to right.
C.
The line falls from left to right.
D.
The line is horizontal.

Answer 1

To find the slope of the line passing through the points \((5, 2)\) and \((6, 4)\), we use the formula for slope \(m\):

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Here, \((x_1, y_1) = (5, 2)\) and \((x_2, y_2) = (6, 4)\). Plugging in these values:

\[
m = \frac{4 - 2}{6 - 5} = \frac{2}{1} = 2
\]

### Part 1
A. The slope is **2**.

### Part 2
Since the slope is positive, the line rises from left to right.

B. The line rises from left to right.