What is the slope of the line that passes through the points (-4, 2) and (-5, 0)? Write your answer in simplest form.

Understand the Problem

The question is asking to calculate the slope of a line that passes through two specific points, (-4, 2) and (-5, 0). The slope can be determined using the formula (y2 - y1) / (x2 - x1).

Answer

The slope is $2$.

Steps to Solve

Identify the Points The given points are $(-4, 2)$ and $(-5, 0)$. We can label these points as follows:

Point 1: $(x_1, y_1) = (-4, 2)$
Point 2: $(x_2, y_2) = (-5, 0)$

Apply the Slope Formula The formula for calculating the slope ($m$) of a line through two points is given by: $$ m = \frac{y_2 - y_1}{x_2 - x_1} $$
Substitute the Values into the Formula Now, substitute the coordinates into the formula: $$ m = \frac{0 - 2}{-5 - (-4)} $$
Simplify the Equation Calculate the difference in the numerator and denominator:

Numerator: $0 - 2 = -2$
Denominator: $-5 + 4 = -1$

Thus, the slope becomes: $$ m = \frac{-2}{-1} $$

Final Calculation Now simplify the fraction: $$ m = 2 $$

The slope of the line is $2$.

More Information

The slope of a line represents the rate of change of $y$ with respect to $x$. A slope of $2$ indicates that for every 1 unit increase in $x$, $y$ increases by 2 units.

Tips

Confusing the order of points: Always remember to use the correct coordinates for $(x_1, y_1)$ and $(x_2, y_2)$.
Not simplifying the fraction completely: Ensure to reduce fractions to their simplest form.

Thank you for voting!