Algebra I 4.5 Graphing Using Slope-Intercept Form.

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Presentation transcript:

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

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

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

Identify the slope and y- intercept of the line with the given equation. x + 4y = 6 EX: Divide by 4 4y4y = – x + 6 Rewrite original equation. Simplify. – x = – x + 6 = 4 y m = -1/4; b = 3/2 – x =

Graph the equation 2x + y = 3. STEP 1 Rewrite the equation in slope-intercept form. y – 2x + 3 = STEP 2 Identify the slope and the y- intercept. = – 2 m and = 3 b STEP 3 Plot the point that corresponds to the y- intercept, (0, 3). STEP 4 Use the slope to locate a second point on the line. Draw a line through the two points.

Graph the equation y = – 2x + 5. = – 2 m and = 5 b y x

Graph the equation x – y – 2 = 0. = 1 m and = -2 b y x

Graph the equation 2x + 3y = 9 =-2/3 m and = 3 b y x

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

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 t seconds. Stairs: d = – 1.75t + 28 Escalator: d = – 2t + 28 Escalators

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

EXAMPLE 3 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. b.