Find the slope of the line containing the points (7, 5) and (2, 4).
A. 1
B. 1/5
C. 7
D. 5
Answer (2)
Assign coordinates: ( x 1 , y 1 ) = ( 7 , 5 ) and ( x 2 , y 2 ) = ( 2 , 4 ) .
Apply the slope formula: m = x 2 − x 1 y 2 − y 1 .
Substitute the coordinates into the formula: m = 2 − 7 4 − 5 .
Simplify to find the slope: m = 5 1 .
5 1
Explanation
Understanding the Problem We are given two points (7, 5) and (2, 4) and asked to find the slope of the line that contains them. 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
Assigning Coordinates Let's assign the coordinates: ( x 1 , y 1 ) = ( 7 , 5 ) and ( x 2 , y 2 ) = ( 2 , 4 ) .
Substituting into the Formula Now, substitute these values into the slope formula: m = 2 − 7 4 − 5
Simplifying the Expression Simplify the expression: m = − 5 − 1 = 5 1
Final Answer Therefore, the slope of the line containing the points (7, 5) and (2, 4) is 5 1 .
Examples
Imagine you're hiking up a hill. The slope is how steep the hill is. If you know two points on the hill (like your starting and ending points), you can calculate the slope to see how much your altitude changes for every step you take forward. A slope of 5 1 means that for every 5 steps you take horizontally, you go up 1 step vertically. This concept is useful in many real-world situations, such as designing roads, ramps, or even understanding the steepness of a ski slope.
The slope of the line connecting the points (7, 5) and (2, 4) is 5 1 . This indicates that for every 5 units moved horizontally, the line moves up 1 unit vertically. Hence, the correct answer is B. 5 1 .
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