What is the slope of the line that contains the points $(7,-1)$ and $(6,-4)$?
Answer (1)
Identify the two points: ( 7 , − 1 ) and ( 6 , − 4 ) .
Apply the slope formula: m = x 2 − x 1 y 2 − y 1 .
Substitute the coordinates: m = 6 − 7 − 4 − ( − 1 ) .
Calculate the slope: m = 3 . The final answer is 3 .
Explanation
Understanding the Problem We are given two points, ( 7 , − 1 ) and ( 6 , − 4 ) , and we want to find the slope of the line that passes through these points.
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
Substituting the Values Let ( x 1 , y 1 ) = ( 7 , − 1 ) and ( x 2 , y 2 ) = ( 6 , − 4 ) . Substituting these values into the slope formula, we get: m = 6 − 7 − 4 − ( − 1 )
Calculating the Slope Simplifying the expression, we have: m = 6 − 7 − 4 + 1 = − 1 − 3 = 3 Therefore, the slope of the line is 3.
Final Answer The slope of the line that contains the points ( 7 , − 1 ) and ( 6 , − 4 ) is 3.
Examples
Imagine you're hiking up a hill. The slope is how steep the hill is. If you know two points on the hill, you can calculate the slope to see how much the height changes for every step you take forward. This is useful in many real-world situations, like designing roads or ramps, where knowing the slope is important for safety and ease of use.
