Problem 94
Question
Describe how to write the equation of a line if the coordinates of two points along the line are known.
Step-by-Step Solution
Verified Answer
The equation of a line for two known points (x1, y1) and (x2, y2) can be written as \( y - y1 = m(x - x1) \), where \( m = \frac{y2 - y1}{x2 - x1} \) is the slope of the line.
1Step 1: Identify the coordinates of the two points
We first need to identify the coordinates of the two points. Suppose the coordinates of the two points are (x1, y1) and (x2, y2).
2Step 2: Find the Slope
Next, we'll find the slope of the line. The slope (m) is given by the formula \( m = \frac{y2 - y1}{x2 - x1} \). This is the difference in y-coordinates (vertical change) divided by the difference in x-coordinates (horizontal change).
3Step 3: Write the Slope-Intercept Form of the Equation
The slope-intercept form of a line equation is \( y = mx + b \), where m is the slope and b is the y-intercept. Substituting our calculated slope and the coordinates of either point (x1, y1) or (x2, y2), we can express the line equation \( y - y1 = m(x - x1) \).
4Step 4: Rearrange the Equation
Finally, rearrange the line equation to the form \( y = mx + b \) for the final equation of the line.
Other exercises in this chapter
Problem 94
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