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1.1 Writing Linear Equations

1.1 Writing Linear Equations. Finding Slope Slope-Intercept Form Point-Slope Form. Finding Slope. The slope of the line that contains (2, 5) and (8, 1). is. Slope. Example 1: Finding Slope by Using the Slope Formula. Find the slope of the line that contains (2, 5) and (8, 1).

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1.1 Writing Linear Equations

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  1. 1.1 Writing Linear Equations Finding Slope Slope-Intercept Form Point-Slope Form

  2. Finding Slope

  3. The slope of the line that contains (2, 5) and (8, 1) is . Slope Example 1: Finding Slope by Using the Slope Formula Find the slope of the line that contains (2, 5) and (8, 1). Use the slope formula. Substitute (2, 5) for (x1, y1) and (8, 1) for (x2, y2). Simplify.

  4. Slope Check It Out! Example 1a Find the slope of the line that contains (–2, –2) and (7, –2). Use the slope formula. Substitute (–2, –2) for (x1, y1) and (7, –2) for (x2, y2). Simplify. = 0 The slope of the line that contains (–2, –2) and (7, –2) is 0.

  5. Slope Check It Out! Example 1b Find the slope of the line that contains (5, –7) and (6, –4). Use the slope formula. Substitute (5, –7) for (x1, y1) and (6, –4) for (x2, y2). Simplify. = 3 The slope of the line that contains (5, –7) and (6, –4) is 3.

  6. Slope Example 2A: Finding Slope from Graphs and Tables The graph shows a linear relationship. Find the slope. Let (0, 2) be (x1, y1) and (–2, –2) be (x2, y2). Use the slope formula. Substitute (0, 2) for (x1, y1) and (–2, –2) for (x2, y2). Simplify.

  7. Slope Check It Out! Example 2a The graph shows a linear relationship. Find the slope. Let (2, 2) be (x1, y1) and (4, 3) be (x2, y2). Use the slope formula. Substitute (2, 2) for (x1, y1) and (4, 3) for (x2, y2). Simplify.

  8. Slope Check It Out! Example 2b The graph shows a linear relationship. Find the slope. Let (–2, 4) be (x1, y1) and (0, –2) be (x2, y2). Use the slope formula. Substitute (–2, 4) for (x1, y1) and (0, –2) for (x2, y2). Simplify.

  9. Slope As shown in the previous examples, slope can be positive, negative, zero or undefined. You can tell which of these is the case by looking at a graph of a line–you do not need to calculate the slope.

  10. Slope Example 4: Finding Slopes of Horizontal and Vertical Lines Find the slope of each line. A. B. You cannot divide by 0 The slope is 0. The slope is undefined.

  11. Slope-Intercept Form

  12. Example 1: Writing the Slope-Intercept Form of the Equation of a Line Write the equation of the graphed line in slope-intercept form. Identify the y-intercept. The y-intercept b is 1. Step 1

  13. 3 4 –4 –3 3 4 Slope is = = – . rise run –3 4 Example 1 Continued Step 2 Find the slope. Choose any two convenient points on the line, such as (0, 1) and (4, –2). Count from (0, 1) to (4, –2) to find the rise and the run. The rise is –3 units and the run is 4 units.

  14. m = – and b = 1. 3 4 The equation of the line is y = – x + 1. y = –x + 1 3 4 3 4 Example 1 Continued Write the equation in slope-intercept form. Step 3 y = mx + b

  15. Check It Out! Example 1 Write the equation of the graphed line in slope-intercept form. Identify the y-intercept. The y-intercept b is 3. Step 1

  16. 3 4 4 3 3 4 Slope is = . rise run Check It Out! Example 1 Continued Step 2 Find the slope. Choose any two convenient points on the line, such as (–4, 0) and (0, 3). Count from (–4, 0) to (0, 3) to find the rise and the run. The rise is 3 units and the run is 4 units 3

  17. m = and b = 3. 3 4 The equation of the line is y = x + 3. y = x + 3 3 4 3 4 Check It Out! Example 1 Continued Write the equation in slope-intercept form. Step 3 y = mx + b

  18. Point-Slope Form

  19. Example 4A: Using Two Points to Write an Equation Write an equation in slope-intercept form for the line through the two points. (2, –3) and (4, 1) Step 1 Find the slope. Step 2 Substitute the slope and one of the points into the point-slope form. y – y1 = m(x – x1) y – (–3) = 2(x – 2) Choose (2, –3).

  20. –3 –3 Example 4A Continued Write an equation in slope-intercept form for the line through the two points. (2, –3) and (4, 1) Step 3 Write the equation in slope-intercept form. y + 3 = 2(x – 2) y + 3 = 2x – 4 y = 2x – 7

  21. Example 4B: Using Two Points to Write an Equation Write an equation in slope-intercept form for the line through the two points. (0, 1) and (–2, 9) Step 1 Find the slope. Step 2 Substitute the slope and one of the points into the point-slope form. y – y1 = m(x – x1) y – 1 = –4(x – 0) Choose (0, 1).

  22. + 1 +1 Example 4B Continued Write an equation in slope-intercept form for the line through the two points. (0, 1) and (–2, 9) Step 3 Write the equation in slope-intercept form. y – 1 = –4(x – 0) y – 1 = –4x y = –4x + 1

  23. Check It Out! Example 4a Write an equation in slope-intercept form for the line through the two points. (1, –2) and (3, 10) Step 1 Find the slope. Step 2 Substitute the slope and one of the points into the point-slope form. y – y1 = m(x – x1) y – (–2) = 6(x – 1) Choose (1, –2). y + 2 = 6(x – 1)

  24. –2 – 2 Check It Out! Example 4a Continued Write an equation in slope-intercept form for the line through the two points. (1, –2) and (3, 10) Step 3 Write the equation in slope-intercept form. y + 2 = 6(x – 1) y + 2 = 6x –6 y = 6x – 8

  25. Check It Out! Example 4b Write an equation in slope-intercept form for the line through the two points. (6, 3) and (0, –1) Step 1 Find the slope. Step 2 Substitute the slope and one of the points into the point-slope form. y – y1 = m(x – x1) Choose (6, 3).

  26. + 3 +3 Check It Out! Example 4b Continued Write an equation in slope-intercept form for the line through the two points. (6, 3) and (0, –1) Step 3 Write the equation in slope-intercept form.

  27. More ExamplesExample 1 Step 2: Find the slope.

  28. More ExamplesExample 1 Continued Notice how they gave you the y-intercept. That means we can use slope-intercept form.

  29. More ExamplesExample 2 Step 2: Find the slope.

  30. More ExamplesExample 2 Continued Notice how they didn’t give you the y-intercept. That means we have to use point-slope form

  31. More ExamplesExample 2 Continued Now we need to simplify Subtracting a negative is really adding Add the 4 to both sides +4 +4

  32. More ExamplesExample 3 You Try Now Write the equation of the line Simply if needed

  33. More ExamplesExample 4 You Try Now Write the equation of the line Simply if needed

  34. More ExamplesAnswer Example 3 Step 2: Find the slope.

  35. More ExamplesAnswer Example 3 Continued Notice how they gave you the y-intercept. That means we can use slope-intercept form.

  36. More ExamplesAnswer Example 4 Step 2: Find the slope.

  37. More ExamplesAnswer Example 4 Continued Notice how they didn’t give you the y-intercept. That means we have to use point-slope form

  38. More ExamplesAnswer Example 4 Continued Now we need to simplify Subtracting a negative is really adding Subtract the 14.2 from both sides -14.2 -14.2

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