Find the slope of the line passing through the points $(-3,6)$ and $(5,6)$.
slope: $\square$
Answer (1)
Identify the coordinates of the two given points: ( − 3 , 6 ) and ( 5 , 6 ) .
Apply the slope formula: m = x 2 − x 1 y 2 − y 1 .
Substitute the coordinates into the formula: m = 5 − ( − 3 ) 6 − 6 .
Simplify to find the slope: m = 0 .
0
Explanation
Understanding the Problem We are given two points, ( − 3 , 6 ) and ( 5 , 6 ) , 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 = − 3 , y 1 = 6 x 2 = 5 , y 2 = 6
Substituting Values Now, substitute these values into the slope formula: m = 5 − ( − 3 ) 6 − 6
Simplifying the Expression Simplify the expression: m = 5 + 3 0 = 8 0 = 0
Final Answer Therefore, the slope of the line passing through the points ( − 3 , 6 ) and ( 5 , 6 ) is 0.
Examples
Understanding the slope is crucial in many real-world applications. For example, when designing a ramp for accessibility, the slope determines how easy it is to use. A slope of 0, as we found in this problem, means the ramp is perfectly flat. In economics, the slope of a cost function can represent the marginal cost, indicating how much it costs to produce one more unit. Similarly, in physics, the slope of a velocity-time graph represents acceleration.
