Find the slope of the line passing through the points $(4,-8)$ and $(9,-8)$.
Answer (1)
Identify the coordinates of the two given points.
Apply the slope formula: m = x 2 − x 1 y 2 − y 1 .
Substitute the coordinates into the formula: m = 9 − 4 − 8 − ( − 8 ) .
Simplify to find the slope: 0 .
Explanation
Understanding the Problem We are given two points, ( 4 , − 8 ) and ( 9 , − 8 ) , and we want to find the slope of the line that passes through them.
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
Identifying Coordinates Let's identify the coordinates: x 1 = 4 , y 1 = − 8 x 2 = 9 , y 2 = − 8
Calculating the Slope Now, substitute these values into the slope formula: m = 9 − 4 − 8 − ( − 8 ) = 5 − 8 + 8 = 5 0 = 0
Final Answer The slope of the line passing through the points ( 4 , − 8 ) and ( 9 , − 8 ) is 0.
Examples
Imagine you're walking on a perfectly flat road. The slope of that road is 0 because you're not going uphill or downhill. Similarly, if you plot your position at two different times on a graph, and the y-coordinates (representing your altitude) are the same, the line connecting those points will have a slope of 0. This concept is useful in various real-world scenarios, such as designing roads, analyzing graphs, and understanding rates of change.
