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Chapter 2: Problem 94

Describe how to write the equation of a line if the coordinates of two points along the line are known.

Short Answer

Expert verified
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.

Step by step solution

01

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).
02

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).
03

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 \( y - y1 = m(x - x1) \).
04

Rearrange the Equation

Finally, rearrange the line equation to the form \( y = mx + b \) for the final equation of the line.

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