What is the slope of the line that passes through the points $(4,0)$ and $(-1,1)$?
Answer (1)
We are given two points (4,0) and (-1,1).
We calculate the slope using the formula m = x 2 − x 1 y 2 − y 1 .
Substituting the given values, we get m = − 1 − 4 1 − 0 = − 5 1 .
The slope of the line is − 5 1 .
Explanation
Understanding the Problem We are given two points, ( 4 , 0 ) and ( − 1 , 1 ) , and we want to find the slope of the line that passes through them.
Recalling the Slope Formula The slope of a line passing through two points ( x 1 , y 1 ) and ( x 2 , y 2 ) is given by the formula: m = x 2 − x 1 y 2 − y 1
Applying the Formula Let's assign the coordinates: x 1 = 4 , y 1 = 0 , x 2 = − 1 , and y 2 = 1 . Now, substitute these values into the slope formula: m = − 1 − 4 1 − 0 = − 5 1 = − 5 1
Final Answer Therefore, the slope of the line that passes through the points ( 4 , 0 ) and ( − 1 , 1 ) is − 5 1 .
Examples
Understanding the slope is crucial in many real-world applications. For instance, if you're analyzing the steepness of a hill on a hiking trail, the slope tells you how much the altitude changes for every unit of horizontal distance. Similarly, in economics, the slope of a supply or demand curve indicates how much the quantity supplied or demanded changes in response to a change in price. Knowing how to calculate and interpret slopes helps in making informed decisions in various fields.
