Question

what is the slope of the line that passes through the points (-4, -10) and (-7, -19)? write your answer in simplest form.

Explanation:

Step1: Recall the slope formula

The slope \( m \) of a line passing through two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify the coordinates

Let \( (x_1, y_1)=(-4, -10) \) and \( (x_2, y_2)=(-7, -19) \).

Step3: Substitute into the formula

Substitute the values into the slope formula: \( m = \frac{-19 - (-10)}{-7 - (-4)} \).
Simplify the numerator and denominator:

• Numerator: \( -19 - (-10)=-19 + 10=-9 \)
• Denominator: \( -7 - (-4)=-7 + 4=-3 \)

So, \( m=\frac{-9}{-3} \).

Step4: Simplify the fraction

Simplify \( \frac{-9}{-3} \) to get \( 3 \).

Answer:

\( 3 \)