What is the slope of the line that passes through the points left parenthesis, minus, 4, comma, minus, 10, right parenthesis(−4,−10) and left parenthesis, minus, 7, comma, minus, 19, right parenthesis(−7,−19)? Write your answer in simplest form.

Answer 1

To find the slope \( m \) of a line that passes through two points \((x_1, y_1)\) and \((x_2, y_2)\), we can use the formula:

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

For the points \((-4, -10)\) and \((-7, -19)\), we assign:

\[ (x_1, y_1) = (-4, -10) \quad \text{and} \quad (x_2, y_2) = (-7, -19) \]

Now, we can substitute these values into the slope formula:

\[ m = \frac{-19 - (-10)}{-7 - (-4)} \]

Simplifying the expressions in the numerator and the denominator:

\[ m = \frac{-19 + 10}{-7 + 4} = \frac{-9}{-3} \]

Now, simplify the fraction:

\[ m = \frac{-9}{-3} = 3 \]

Thus, the slope of the line that passes through the points \((-4, -10)\) and \((-7, -19)\) is

\[ \boxed{3} \]