Find the slope of the line passing through the points $(-7,9)$ and $(-7,-8)$.
Answer (1)
Identify the coordinates of the two points: ( − 7 , 9 ) and ( − 7 , − 8 ) .
Apply the slope formula: m = x 2 − x 1 y 2 − y 1 .
Substitute the coordinates into the formula: m = − 7 − ( − 7 ) − 8 − 9 = 0 − 17 .
Since division by zero is undefined, the slope is undefined, indicating a vertical line. undefined
Explanation
Understanding the Problem We are given two points ( − 7 , 9 ) and ( − 7 , − 8 ) and asked to find the slope of the line passing through them.
Recalling the Slope Formula The slope m 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 = − 7 , y 1 = 9 x 2 = − 7 , y 2 = − 8
Substituting into the Formula Now, substitute these values into the slope formula: m = − 7 − ( − 7 ) − 8 − 9 = − 7 + 7 − 17 = 0 − 17
Determining the Slope Since division by zero is undefined, the slope of the line is undefined. This means the line is vertical.
Examples
Imagine you're climbing a perfectly vertical cliff. The slope represents how steep the climb is. In this case, since the cliff is vertical, the slope is undefined because you're not moving horizontally at all – just straight up! This concept is useful in various real-world scenarios, such as designing structures, mapping terrains, and understanding rates of change.
