Find the slope of the line passing through the points $(-9,5)$ and $(6,5)$.
Answer (1)
Identify the coordinates of the two points: ( − 9 , 5 ) and ( 6 , 5 ) .
Apply the slope formula: m = x 2 − x 1 y 2 − y 1 .
Substitute the coordinates into the formula: m = 6 − ( − 9 ) 5 − 5 .
Simplify to find the slope: m = 0 . The final answer is 0 .
Explanation
Understanding the Problem We are given two points, ( − 9 , 5 ) and ( 6 , 5 ) , 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 where m represents the slope.
Identifying Coordinates Let's identify the coordinates: x 1 = − 9 , y 1 = 5 x 2 = 6 , y 2 = 5
Substituting Values Now, substitute these values into the slope formula: m = 6 − ( − 9 ) 5 − 5
Simplifying the Expression Simplify the expression: m = 6 + 9 0 = 15 0 = 0
Final Answer Therefore, the slope of the line passing through the points ( − 9 , 5 ) and ( 6 , 5 ) is 0.
Examples
Understanding the slope of a line is crucial in many real-world applications. For example, consider a ramp for wheelchair access. If the slope is too steep, it becomes difficult to use. If the height of the ramp is 1 foot and the horizontal distance is 12 feet, the slope is 12 1 . Similarly, in construction, knowing the slope of a roof is essential for proper water runoff. A roof with a slope of 0 is flat, while a roof with a higher slope will shed water more effectively. Understanding slope helps in designing safe and functional structures.
