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Learn how to write equations of lines in various forms, including slope-intercept form and point-slope form. Understand how to determine the slope and y-intercept from given points or slopes. Practice writing equations of lines parallel or perpendicular to given lines.
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Page 86 2.4: Writing Equations of Lines
Page 93 2.4: Writing Equations of Lines
Writing Equations of Lines Section 2.4 2.4: Writing Equations of Lines
Equations Slope Equation: 2.4: Writing Equations of Lines
Recall Slope Y-intercept 2.4: Writing Equations of Lines
Example 1 Graph y = –2x + 3 y = mx + b y = mx + 3 2.4: Writing Equations of Lines
Example 1 Graph y = –2x + 3 y = mx + b y = mx + 3 y = –2x + 3 2.4: Writing Equations of Lines
Example 2 Graph y= –1/2x – 5/2 2.4: Writing Equations of Lines
Example 3 Graph y = 4, identify slope and y-intercept Slope: Zero Y-intercept: (0, 4) 2.4: Writing Equations of Lines
Your Turn Graph x = –1, identify slope and y-intercept Slope: No Slope or Undefined Y-intercept: None 2.4: Writing Equations of Lines
Point-Slope Equation X1is the x-coordinate Y1is the y-coordinate Slope 2.4: Writing Equations of Lines
Example 4 Given below: Write an equation in Point-Slope Form. 2.4: Writing Equations of Lines
Example 4 What are the two points given? (4, 0) and (0, –2) What is the slope of this equation? m = 1/2 2.4: Writing Equations of Lines
Example 4 If a point and a slope is given, use the point-slope formula y – y1 = m (x – x1) 2.4: Writing Equations of Lines
Example 4 y – y1 = m (x – x1) y – (–2) = ½ (x – 0) y + 2 = 1/2x y = 1/2x – 2 2.4: Writing Equations of Lines
Example 5 Given point (4, –2) and the graph below, write the equation 2.4: Writing Equations of Lines
Example 5 What is a point given? (4, –2) and (0, 3) What is the slope of this equation? m= –5/4 2.4: Writing Equations of Lines
Example 5 y – y1 = m (x – x1) y – (3) = –5/4(x – 0) y - 3 = –5/4x 2.4: Writing Equations of Lines
Example 6 Given point (–1, –5) and the slope of ¾, write an equation in Point-Slope Form y – y1 = m (x – x1) y – (–5) = 3/4 (x – (–1)) y + 5 = ¾(x +1) y = 3/4x –17/4 2.4: Writing Equations of Lines
Your Turn If given point (–1, –4) and the slope of 7/2, draw the graph and write the equation in Point-Slope Form 2.4: Writing Equations of Lines
Example 7 Determine an equation of the line containing the points (2, 3) and (–4, 5) What equations will you need? 2.4: Writing Equations of Lines
Example 7 Determine an equation of the line containing the points (2, 3) and (–4, 5). What equations will you need? 2.4: Writing Equations of Lines
Example 8 Determine an equation of the line containing the points (2, 5) and (–3, 4). 2.4: Writing Equations of Lines
Your Turn Determine an equation of the line containing the points (3, 12) and (6, 27). 2.4: Writing Equations of Lines
Given Point and Equation • Rewrite the equation in Y-intercept form • Apply the appropriate slope • Plug in points using Point-Slope form • Simplify Remember: PARALLEL: SAME SLOPES PERPENDICULAR: OPPOSITE SIGN RECIPROCAL 2.4: Writing Equations of Lines
Review Line 1 contains points of (0, 5) and (2, 0) Line 2 contains points of (5, 0) and (0, –2) Is it parallel, perpendicular, or neither? PERPENDICULAR 2.4: Writing Equations of Lines
Write an equation of the line that passes through (–2, 3) and is (a) parallel and (b) perpendicular to the line y = –4x + 1. Write answers in Point-Slope form. Example 9 2.4: Writing Equations of Lines
Example 10 Write an equation of the line in slope-intercept form which is parallel to the line 2x + y =10and containing the point (–1, 3). 2.4: Writing Equations of Lines
Your Turn Write an equation of the line in slope-intercept form which is perpendicular to 4y – x = 20 and containing the point (2, –3). 2.4: Writing Equations of Lines
Assignment: Pg 101: 3-39 odd, 46 9-17: Leave your answers in point-slope form 7/21/2012 12:49 AM 2-4: Writing Linear Functions 2.4: Writing Equations of Lines 31
