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Understanding Parallel Lines and Slope-Intercept Form

In this lesson, you'll learn how to determine whether lines are parallel and how to write their equations in slope-intercept form (y = mx + b). We will practice writing equations, finding x and y intercepts, and analyzing graphs to confirm parallelism. By understanding the conditions for parallel lines—specifically that they have the same slope—you will develop essential skills in algebra. Exercise problems will reinforce your knowledge, including finding slopes of parallel lines and writing equations that pass through given points.

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Understanding Parallel Lines and Slope-Intercept Form

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  1. WARM- UP! • 1.Write the equation in slope-intercept form • 2x + y = 4 • 2.Write the x and y intercept of 2x + 3y = 6

  2. OBJECTIVES: Determining whether lines are parallel Writing equations of parallel lines 2/ 17/11

  3. PARALLEL LINES • Lines in the same place that never intersect are called parallel lines • Two lines are parallel if they have the same slope. • Use Slope-intercept form • y = mx + b

  4. Ex. Are the graphs of these 2 lines parallel? • 3y = 2x + 15 Solution: Write the two equations in slope- intercept form • 3y = 2x + 15 3 3 y = ⅔ x + 5 The two lines are parallel • 2x – 3y = 3 • 2x – 3y = 3 -2x -2x - 3y = -2x +3 -3 -3 y = ⅔ x - 1

  5. Example #2 Are the graphs of these 2 lines parallel? • x + 2y = 7 Solution: Write the two equations in slope- intercept form • -2x + y = 3

  6. EQUTIONS OF PARALLEL LINES • Two lines are parallel if they have the same slope. • Example #1. Write the equation of a line that passes through ( -1, 3) and is parallel to 5x + y = 2 Step 1. Find the slope of the other line. Write the equation in slope-intercept form y = mx + b 5 x + y = 2 -5x -5x the two lines are parallel y = -5x + 2 so they have the same slope, m = -5

  7. Step 2: Solve for b y = mx + b 3 = -5( -1) + b 3 = 5 + b -5 = -5 -2 = b • Step 3: Plug-in the values of m and b y = mx + b y = -5x – 2

  8. WORK TIME:#1. Find the slope of a line parallel to the graph of 5x + y = 7.

  9. #2.Write an equation for the line that is parallel to y = 2x + 6 and passes through (–1, 5).

  10. #3. Are the lines –7x – 8y = 0 and –7x – 8y = –3 parallel ?

  11. #4. Find the slope of a line parallel to the graph of 4x – y = 8.

  12. WORK TIME: 15 MINUTES ONLY! Nothing will work unless you do.

  13. SOLO TIME: I AM PROUD OF MYSELF I AM A GOOD STUDENT WITH RESPECT FOR ME AND OTHERS.

  14. EXIT PASS: • WRITE TWO EQUATIONS THAT ARE PARALLEL

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