Question

find the slope of the line that passes through (4, -10) and (5, 16). simplify your answer and write it as a proper fraction, improper fraction, or integer.

Explanation:

Step1: Recall the slope formula

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Here, \( x_1 = 4 \), \( y_1=- 10 \), \( x_2 = 5 \), \( y_2 = 16 \).

Step2: Substitute the values into the formula

Substitute the values into the slope formula: \( m=\frac{16-(-10)}{5 - 4} \).
Simplify the numerator: \( 16-(-10)=16 + 10=26 \).
Simplify the denominator: \( 5 - 4 = 1 \).

Step3: Calculate the slope

So, \( m=\frac{26}{1}=26 \).

Answer:

26