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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 the line passing through two known points can be found by first calculating the slope \(m\) between the two points and then substituting this slope and one of the points into the point-slope form \(y - y_1 = m(x - x_1)\) to write the equation. The equation is then simplified to the slope-intercept form \(y = mx + c\).

Step by step solution

01

Find the Slope

To find the slope \(m\) of the line that passes through two points \((x_1, y_1)\) and \((x_2, y_2)\), use the formula: \(m = (y_2 - y_1) / (x_2 - x_1)\). It's important to substitute the given coordinates into this formula correctly.
02

Substitute in the Point-Slope Formula

Use the point-slope form of an equation, \(y - y_1 = m(x - x_1)\), and substitute one of the points and the slope into this formula to write the equation of the line. Any point along the line can be used here. Substitute the x and y values of the chosen point into \(x_1\) and \(y_1\) in the formula, and the calculated slope into \(m\).
03

Simplify the Equation

Rearrange and simplify the equation obtained in Step 2 to obtain the equation of the line in slope-intercept form \(y = mx + c\), where \(m\) is the slope and \(c\) is the y-intercept.

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