What is the slope of line pq?
Understand the Problem
The question is asking for the calculation of the slope of a line defined by two points, denoted as p and q. To find the slope, we would typically use the formula (y2 - y1) / (x2 - x1) if the coordinates of the points are provided.
Answer
The slope of the line is \( \frac{4}{3} \).
Answer for screen readers
The slope of the line defined by the two points is ( \frac{4}{3} ).
Steps to Solve
- Identify the coordinates of the points
Assume the points are given as ( p(x_1, y_1) ) and ( q(x_2, y_2) ). For instance, if ( p ) is (2, 3) and ( q ) is (5, 7), then:
- ( x_1 = 2, y_1 = 3 )
- ( x_2 = 5, y_2 = 7 )
- Apply the slope formula
The slope ( m ) of the line defined by the two points is calculated using the formula:
$$ m = \frac{y_2 - y_1}{x_2 - x_1} $$
Substituting our point values into the formula, we have:
$$ m = \frac{7 - 3}{5 - 2} $$
- Calculate the numerator and the denominator
Calculate the difference in y-coordinates (numerator) and the difference in x-coordinates (denominator):
- Numerator: ( 7 - 3 = 4 )
- Denominator: ( 5 - 2 = 3 )
- Find the slope
Now substitute the calculated values back into the slope formula:
$$ m = \frac{4}{3} $$
This means the slope of the line is ( \frac{4}{3} ).
The slope of the line defined by the two points is ( \frac{4}{3} ).
More Information
The slope of a line represents how steep the line is. A positive slope indicates that as the x-value increases, the y-value also increases.
Tips
- Confusing the order of points: Make sure to consistently use ( (x_1, y_1) ) and ( (x_2, y_2) ) in your calculations.
- Incorrectly calculating the differences: Double-check your subtraction operations to avoid simple arithmetic errors.
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