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 of how steep the line is. It's found by measuring the vertical change (the 'rise') for a given horizontal change (the 'run'). The formula for finding the slope of a line when given two points (\(x_1\), \(y_1\)) and (\(x_2\), \(y_2\)) on the line is \(m = \frac{{y_2 - y_1}}{{x_2 - x_1}}\).
1Step 1: Understand the Concept of Slope
The slope of a line in a plane is a measure of how steep the line is. It's a measure of the vertical change (rise) for a given horizontal change (run). It's represented by the letter 'm'.
2Step 2: The Formula for Slope
The formula for finding the slope of a line when given two points, (\(x_1\), \(y_1\)) and (\(x_2\), \(y_2\)), on the line is \(m = \frac{{y_2 - y_1}}{{x_2 - x_1}}\). This finds the 'rise over run', or the change in the y-coordinates divided by the change in the x-coordinates.
3Step 3: Applying the Formula
To apply the formula, subtract the y-coordinates of the two points from each other to get the 'rise'. Then, subtract the x-coordinates of the two points from each other to get the 'run'. Finally divide the 'rise' by the 'run' to get the slope.
Other exercises in this chapter
Problem 93
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Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The domain of \(f\) is t
View solution Problem 94
Begin by graphing the absolute value function, \(f(x)-|x| .\) Then use transformations of this graph to graph the given function. $$ g(x)--2|x+3|+2 $$
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