Which gives the slope of the line containing the points (2, 7) and (3, 4)?
Understand the Problem
The question is asking for the calculation of the slope of a line defined by two given points (2, 7) and (3, 4). The slope is typically found using the formula (y2 - y1) / (x2 - x1).
Answer
The slope of the line is \( m = -3 \).
Answer for screen readers
The slope of the line containing the points ( (2, 7) ) and ( (3, 4) ) is ( m = -3 ).
Steps to Solve
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Identify the points The two points given are ( (x_1, y_1) = (2, 7) ) and ( (x_2, y_2) = (3, 4) ).
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Use the slope formula The formula to calculate the slope ( m ) between two points is given by:
$$ m = \frac{y_2 - y_1}{x_2 - x_1} $$
- Substitute the values Plugging in the coordinates of the points into the formula:
$$ m = \frac{4 - 7}{3 - 2} $$
- Perform the calculations Now, calculate the value:
$$ m = \frac{-3}{1} = -3 $$
- State the final slope The slope of the line containing the points ( (2, 7) ) and ( (3, 4) ) is ( m = -3 ).
The slope of the line containing the points ( (2, 7) ) and ( (3, 4) ) is ( m = -3 ).
More Information
The slope represents the rate of change of ( y ) with respect to ( x ). A negative slope indicates that as ( x ) increases, ( y ) decreases.
Tips
- Confusing the order of the points when substituting into the slope formula. Remember to consistently use ( (x_1, y_1) ) and ( (x_2, y_2) ) in that order.
- Forgetting to calculate carefully when subtracting, which can lead to incorrect slope values.
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