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

b. the slope is undefined.

Explanation:

Step1: Recall the slope formula

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

Step2: Identify the coordinates

For the points \( (4, 3) \) and \( (5, 7) \), we have \( x_1 = 4 \), \( y_1 = 3 \), \( x_2 = 5 \), \( y_2 = 7 \).

Step3: Substitute into the formula

Substitute the values into the slope formula: \( m=\frac{7 - 3}{5 - 4} \).

Step4: Simplify the expression

Simplify the numerator and the denominator: \( 7 - 3 = 4 \) and \( 5 - 4 = 1 \), so \( m=\frac{4}{1}=4 \).
Since the slope is positive, the line rises from left to right.

Answer:

A. The slope is \( 4 \).