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.
(4,3) and (5,7)
select the correct choice below and, if necessary, fill in the answer box within your choice.
a. the slope is 4.
b. the slope is undefined.
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 is horizontal.
d. the line falls from left to right.

Explanation:

For the slope calculation:

Step1: Recall the slope formula

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Here, \( (x_1, y_1)=(4, 3) \) and \( (x_2, y_2)=(5, 7) \).

Step2: Substitute the values into the formula

Substitute \( x_1 = 4 \), \( y_1 = 3 \), \( x_2 = 5 \), and \( y_2 = 7 \) into the formula:
\( m=\frac{7 - 3}{5 - 4} \)

Step3: Simplify the numerator and denominator

Simplify the numerator: \( 7 - 3 = 4 \)
Simplify the denominator: \( 5 - 4 = 1 \)
So, \( m=\frac{4}{1}=4 \)

For the direction of the line:

A positive slope means the line rises from left to right, a negative slope means it falls from left to right, a slope of 0 means it is horizontal, and an undefined slope means it is vertical. Since the slope \( m = 4 \) is positive, the line rises from left to right.

Answer:

s:

• The slope is \( \boldsymbol{4} \).
• The line rises from left to right (Option B).