Problem 93
Question
What is the slope of a line and how is it found?
Step-by-Step Solution
Verified Answer
The slope of a line is a measure that indicates the direction and 'steepness' of a line on a coordinate plane. It is calculated as the change in the 'y' coordinate divided by the change in the 'x' coordinate for any two points on the line, typically expressed as 'rise over run' using the formula \((y_2 - y_1) / (x_2 - x_1)\).
1Step 1: Definition of Slope
The slope of a line is a measure of the amount that the line rises (or falls) for each unit it runs to the right. It indicates the direction and the steepness of a line on a coordinate plane. A positive slope indicates that the line rises from left to right, while a negative slope indicates that the line falls from left to right. A slope of 0 means the line is horizontal.
2Step 2: Formula for Slope
The formula for slope is \((y_2 - y_1) / (x_2 - x_1)\). This is sometimes referred to as 'rise over run'. Here, \((x_1 , y_1)\) and \((x_2 , y_2)\) are any two points on the line.
3Step 3: Calculating Slope
In order to compute the slope, two points on the line are needed. Subtract the 'y' coordinates (rise) and the 'x' coordinates (run) of these two points respectively. Then the slope 'm' is given by the formula, \(m = (rise)/(run) = (y_2 - y_1) / (x_2 - x_1)\)
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Problem 93
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