A line intersects the points [tex]$(6,-4) \text { and } (7,4) \text {. }$[/tex]
What is the slope of this line in simplest form?
[tex]$m=[?]$[/tex]
Answer (2)
Identify the coordinates of the two points: ( 6 , − 4 ) and ( 7 , 4 ) .
Apply the slope formula: m = x 2 − x 1 y 2 − y 1 .
Substitute the coordinates into the formula: m = 7 − 6 4 − ( − 4 ) .
Simplify to find the slope: m = 8 .
The slope of the line is 8 .
Explanation
Understanding the Problem We are given two points on a line, ( 6 , − 4 ) and ( 7 , 4 ) , and we need to find the slope of this line.
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
Identifying the Coordinates Let's identify the coordinates: x 1 = 6 , y 1 = − 4 x 2 = 7 , y 2 = 4
Substituting the Values Now, substitute these values into the slope formula: m = 7 − 6 4 − ( − 4 )
Simplifying the Expression Simplify the expression: m = 7 − 6 4 + 4 = 1 8 = 8
Final Answer Therefore, the slope of the line is 8.
Examples
Imagine you're hiking up a hill. The slope represents how steep the hill is. If the slope is 8, it means for every 1 unit you move horizontally, you move 8 units vertically. This concept is also used in construction to design ramps or roofs, ensuring they have the correct angle.
The slope of the line passing through the points (6, -4) and (7, 4) is 8. This is calculated using the slope formula by substituting the coordinates and simplifying the expression. Therefore, the slope can be expressed as m = 8.
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