2.4: Writing Equations of Lines Page 86 18) Perpendicular 19) Neither 20) Parallel 21) 22) 23) 24) $6/hr 25) 13 mi/gallon 26) 4 ft/sec 27) 2 m/sec 29) 2 31) 1/6 33) -3/2 12/7/2018 11:21 PM 2.4: Writing Equations of Lines

2.4: Writing Equations of Lines Page 93 3) Slope is 3 times the P.F. 7) Slope is 2x and the P.F. and down 1 11) 15) 19) 23) C 24) X-int.: (4, 0), Y-int.: (0, –4) 25) X-int.: (–15, 0), Y-int.: (0, –3) 26) X-int.: (–4, 0), Y-int.: (0, 3) 27) X-int.: (5, 0), Y-int.: (0, –10) 28) X-int.: (5, 0), Y-int.: (0, –4) 29) X-int.: (6, 0), Y-int.: (0, –4.5) 30) 45) 49) 53) 57) Slope: -A/B; Y-int.: (0, C/B) 12/7/2018 11:21 PM 2.4: Writing Equations of Lines

2.4: Writing Equations of Lines 12/7/2018 11:21 PM 2.4: Writing Equations of Lines

Writing Equations of Lines Section 2.4 12/7/2018 11:21 PM 2.4: Writing Equations of Lines

2.4: Writing Equations of Lines Slope Equation: 12/7/2018 11:21 PM 2.4: Writing Equations of Lines

2.4: Writing Equations of Lines Recall Slope Y-intercept 12/7/2018 11:21 PM 2.4: Writing Equations of Lines

2.4: Writing Equations of Lines Example 1 Graph y = –2x + 3 y = mx + b y = mx + 3 12/7/2018 11:21 PM 2.4: Writing Equations of Lines

2.4: Writing Equations of Lines Example 1 Graph y = –2x + 3 y = mx + b y = mx + 3 y = –2x + 3 12/7/2018 11:21 PM 2.4: Writing Equations of Lines

2.4: Writing Equations of Lines Example 2 Graph y = –1/2x – 5/2 12/7/2018 11:21 PM 2.4: Writing Equations of Lines

2.4: Writing Equations of Lines Example 3 Graph y = 4, identify slope and y-intercept Slope: Zero Y-intercept: (0, 4) 12/7/2018 11:21 PM 2.4: Writing Equations of Lines

Your Turn Graph x = –1, identify slope and y-intercept Slope: No Slope or Undefined Y-intercept: None 12/7/2018 11:21 PM 2.4: Writing Equations of Lines

2.4: Writing Equations of Lines Point-Slope Equation X1 is the x-coordinate Y1 is the y-coordinate Slope 12/7/2018 11:21 PM 2.4: Writing Equations of Lines

2.4: Writing Equations of Lines Example 4 Given below: Write an equation in Point-Slope Form. 12/7/2018 11:21 PM 2.4: Writing Equations of Lines

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 12/7/2018 11:21 PM 2.4: Writing Equations of Lines

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) 12/7/2018 11:21 PM 2.4: Writing Equations of Lines

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 12/7/2018 11:21 PM 2.4: Writing Equations of Lines

2.4: Writing Equations of Lines Example 5 Given point (4, –2) and the graph below, write the equation 12/7/2018 11:21 PM 2.4: Writing Equations of Lines

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 12/7/2018 11:21 PM 2.4: Writing Equations of Lines

2.4: Writing Equations of Lines Example 5 y – y1 = m (x – x1) y – (3) = –5/4(x – 0) y - 3 = –5/4x 12/7/2018 11:21 PM 2.4: Writing Equations of Lines

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 12/7/2018 11:21 PM 2.4: Writing Equations of Lines

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 12/7/2018 11:21 PM 2.4: Writing Equations of Lines

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? 12/7/2018 11:21 PM 2.4: Writing Equations of Lines

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? 12/7/2018 11:21 PM 2.4: Writing Equations of Lines

2.4: Writing Equations of Lines Example 8 Determine an equation of the line containing the points (2, 5) and (–3, 4). 12/7/2018 11:21 PM 2.4: Writing Equations of Lines

2.4: Writing Equations of Lines Your Turn Determine an equation of the line containing the points (3, 12) and (6, 27). 12/7/2018 11:21 PM 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 12/7/2018 11:21 PM 2.4: Writing Equations of Lines

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 12/7/2018 11:21 PM 2.4: Writing Equations of Lines

2.4: Writing Equations of Lines Example 9 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. Parallel Perpendicular 12/7/2018 11:21 PM 2.4: Writing Equations of Lines 28

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 = 10 and containing the point (–1, 3). 12/7/2018 11:21 PM 2.4: Writing Equations of Lines

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). 12/7/2018 11:21 PM 2.4: Writing Equations of Lines

Assignment: Pg 101: 3-39 odd, 46 9-17: Leave your answers in point-slope form 12/7/2018 11:21 PM 2-4: Writing Linear Functions 12/7/2018 11:21 PM 2.4: Writing Equations of Lines 31