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 $2$.
Answer for screen readers
The slope of the line 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: $(x_2, y_2) = (-5, 0)$
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Apply the Slope Formula The formula for calculating the slope ($m$) of a line through two points is given by: $$ m = \frac{y_2 - y_1}{x_2 - x_1} $$
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Substitute the Values into the Formula Now, substitute the coordinates into the formula: $$ m = \frac{0 - 2}{-5 - (-4)} $$
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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.
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