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Algebra I

Algebra I. 4.5 Graphing Using Slope-Intercept Form. Vocabulary. Slope Intercept Form: y = mx + b; where m is the slope and b is the y-intercept Parallel: 2 lines in the same plane that do not intersect. y = 3 x + 4. y = 5 x – 3. 3 x + y = 2. 1. 3. 2.

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Algebra I

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  1. Algebra I 4.5 Graphing Using Slope-Intercept Form

  2. Vocabulary • Slope Intercept Form: y = mx + b; where m is the slope and b is the y-intercept • Parallel: 2 lines in the same plane that do not intersect

  3. y = 3x + 4 y = 5x – 3 3x +y = 2 1. 3. 2. Identify the slope and y-intercept of the line with the given equation. y = -3x + 2, so m = -3, b = 2 m = 3, b = 4 m = 5, b = -3

  4. y y 3x + 12 x – 4 EX: 3x – 3y = 12 =- -3 = Identify the slope and y-intercept of the line with the given equation. -3y = -3x + 12 Rewrite original equation. Divide by - 3. Simplify.

  5. – x + 6 EX: x + 4y = 6 4y =– x + 6 y = 4 6 – x 3 – x + + = = 4 4 4 2 Identify the slope and y-intercept of the line with the given equation. Rewrite original equation. Divide by 4 Simplify. m = -1/4; b = 3/2

  6. = 3 = – 2 b m and – 2x + 3 y = Graph the equation2x +y = 3. STEP1 Rewrite the equation in slope-intercept form. STEP2 Identify the slope and the y-intercept. STEP3 Plot the point that corresponds to the y-intercept,(0, 3). Use the slope to locate a second point on the line. Draw a line through the two points. STEP4

  7. = – 2 = 5 m b and y 10 x -10 -10 10 Graph the equationy =– 2x + 5.

  8. = 1 = -2 m b and y 10 x -10 -10 10 Graph the equationx – y – 2 = 0.

  9. =-2/3 = 3 m b and y 10 x -10 -10 10 Graph the equation2x + 3y = 9

  10. = 8 – 4 5 –3 2 = 4 2 – 4 = 8 3+1 – 2 2 – (–2) 2+2 4 –2 = = 1 1 – 1 – (– 9) –1+ 9 = 2 2 3 –(1) = Determine which lines are parallel by finding the slope of each line: line a through (-1, 2) and (3, 4) line b through (3, 4) and (5, 8) line c through (-9, -2) and (-1, 2) Line a: m= Line b: m= Line c: m=

  11. Stairs: Escalator: d =– 1.75t + 28 d =– 2t + 28 Escalators To get from one floor to another at a library, you can take either the stairs or the escalator. You can climb stairs at a rate of 1.75 feet per second, and the escalator rises at a rate of 2 feet per second. You have to travel a vertical distance of 28 feet. The equations model the vertical distance d(in feet) you have left to travel after tseconds.

  12. a. Graph the equations in the same coordinate plane. b. How much time do you save by taking the escalator? SOLUTION a. Draw the graph of d= – 1.75t + 28 using the fact that the d-intercept is28 and the slope is – 1.75. Similarly, draw the graph of d=– 2t + 28. The graphs make sense only in the first quadrant.

  13. b. The equation d=–1.75t+28 has a t-intercept of 16. The equation d=–2t+28 has a t-intercept of 14. So, you save 16 –14=2 seconds by taking the escalator. EXAMPLE 3

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