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Writing Linear Equations from Two Points: A Step-by-Step Guide

Learn how to write a linear equation in the form y = mx + b using just two given points. This guide walks you through the essential steps: first, calculate the slope (m) using rise over run. Then, select one point to find the y-intercept (b). Two examples illustrate how to handle different cases, including vertical and horizontal lines. By the end of this lesson, you'll confidently create the equation of a line, no matter the circumstances.

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Writing Linear Equations from Two Points: A Step-by-Step Guide

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  1. How in the world do I write a linear equation when all I’m given is two points? y=mx + b

  2. Steps • Find the slope using rise over run • Use either one of the two points (x, y) and the slope to find the y-intercept (b). We did this yesterday! • Write the equation in y = mx + b form.

  3. Example 1 • Write the equation of a line passing through (4, 8) and (-8, 4). • Find the slope first • m = (8 – 4)/(4 - -8) • m = 4/12 • m = 1/3

  4. Example 1 (cont) • Step 2 • Choose either one of the two points, it doesn’t matter which one. • Use it and the slope from Step 1 to find the y-intercept. Remember, we did this yesterday

  5. Example 1 (cont) • We will use the first point (4, 8) and the slope of 1/3. • y = mx + b • 8 = 1/3(4) + b • 8 = 4/3 + b • b = 20/3

  6. Example 1 (cont) • Now you can write the equation.

  7. Example 2 (Special Case) • Write the equation of a line passing through (3, -8) and (3, -2). • Find the slope first • m = (-8 – -2)/(3 - 3) • m = -6/0 • m = undefined

  8. Example 2 (cont) • When the slope is undefined, you should recall that the graph of it is a vertical line. • Vertical lines cross the x-axis. • Since the line crosses the x-axis only, choose the value of x and write your equation. • x = 3

  9. Example 3 (special case) • Write the equation of a line passing through (5, -2) and (3, -2). • Find the slope first • m = (-2 - -2)/(5 - 3) • m = 0/2 • m = zero

  10. Example 3 (cont) • When the slope is zero, you should recall that the graph of it is a horizontal line. • Horizontal lines cross the y-axis. • Since the line crosses the y-axis only, choose the value of y and write your equation. • y = -2

  11. The End • I hope you enjoyed today’s lesson. You should now know what to do when you are asked to write the equation of a line given two points.

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