What is the slope of the line that goes through the points $(-4,5)$ and $(6,2)$?
A. 6
B. $-10 / 3$
C. $-3 / 2$
D. $-3 / 10$
Answer (2)
The slope formula is m = x 2 − x 1 y 2 − y 1 .
Substitute the given points ( − 4 , 5 ) and ( 6 , 2 ) into the formula.
Calculate the slope: m = 6 − ( − 4 ) 2 − 5 = 10 − 3 .
The slope of the line is − 10 3 .
Explanation
Understanding the Problem and Formula We are given two points on a line, ( − 4 , 5 ) and ( 6 , 2 ) , and we want to find the slope of the line. 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.
Substituting the Values Let's identify the coordinates of our points: ( x 1 , y 1 ) = ( − 4 , 5 ) and ( x 2 , y 2 ) = ( 6 , 2 ) .
Now, we substitute these values into the slope formula: m = 6 − ( − 4 ) 2 − 5
Simplifying the Expression Now, we simplify the expression: m = 6 + 4 − 3 = 10 − 3 = − 10 3 So, the slope of the line is − 10 3 .
Final Answer Therefore, the slope of the line that goes through the points ( − 4 , 5 ) and ( 6 , 2 ) is − 10 3 .
Examples
Imagine you are hiking on a trail that goes through two points. If you know the coordinates of these points, you can calculate the slope of the trail. The slope tells you how steep the trail is. A negative slope means you are going downhill, while a positive slope means you are going uphill. Knowing the slope can help you estimate the effort required to hike the trail.
The slope of the line that goes through the points ( − 4 , 5 ) and ( 6 , 2 ) is − 10 3 , calculated using the slope formula. This indicates a downward slope. The correct answer is option D: − 10 3 .
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