Geometry 13.7 Writing Linear Equations. Slope Intercept Form Write an equation of the line whose slope m is -2 and whose y-intercept b is 5. m = -2 b.

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Presentation transcript:

Geometry 13.7 Writing Linear Equations

Slope Intercept Form Write an equation of the line whose slope m is -2 and whose y-intercept b is 5. m = -2 b = 5 y = mx + b y = -2x + 5 Complete exercises #1-3 in Part I and check below. 1. y = 2x y = -½x y = -2/3x + 1/3

Point Slope Form (PS) Today we will use this formula to find the equation of a line when you are only given either: the slope and one point on the line. two points on the line.

III. Given Point and Slope 1) (2, 5); m = 4

(2, 5) (0,-3) Step 1: Use PS Form Step 2: Simplify to SI Form y - 5 = 4x y = 4x - 3 Using (2, 5) and m = 4 Part III #1: Given point and slope.

-6 y = -2/3x Using (6, -6) and m = -2/3 Part III- Do #2 and #3: Given point and slope. y = -½x Using (-4, 0) and m = -½

IV. Given Two Points 1) (1, 2); (4, 7)

Step 1: Compute slope Step 2: Use PS Form Step 3: Simplify to SI Form +2 y = 5/3x + 1/3 Using (1, 2) Part IV #1: Given 2 points.(1,2) and (4,7) You can check with other point: 7 = 5/3(4) + 1/3 7 = 20/3 + 1/3 7 = 21/3 7 = 7 check!

Now you try #2 and #3. Write the equation of the line through the two given points. 2. (2, 5) and (1, -2) m = 7 PS: y - 5 = 7(x – 2) or y + 2 = 7(x - 1) SI: y = 7x (-2, -4) and (-3, -1) m = -3 PS: y + 4 = -3(x + 2) or y + 1 = -3(x + 3) SI: y = -3x - 10

II. Given x- and y- intercepts 1) x-int. = 2; y-int. = -32) x-int. = –4; y-int. = 33) x-int. = –3; y-int. = –7

Horizontal Lines x y y = 5 y = 3 y = -2 y = -6 Horizontal lines are all parallel to each other and perpendicular to all vertical lines. Horizontal lines all have a slope of 0.

Vertical Lines x y x = 5x = 3 x = -2 x = -6 Vertical lines are all parallel to each other and perpendicular to all horizontal lines. Vertical lines all have a slope that is UNDEFINED.

y = x - 11 Part VI #1: Point and parallel or perpendicular line. (9,-2) and parallel to y = x + 3 Use (9,-2) and the same slope of m = 1 Use PS form: y + 2 = 1(x – 9) y + 2 = x - 9 Check: -2 = = -2check!

y = 2/3x + 5 Part VI #3: Point and parallel or perpendicular line. (-6,1) and perpendicular to y = -3/2x - 1 Use (-6,1) and the opposite reciprocal slope of m = 2/3 Use PS form: y - 1 = 2/3(x + 6) y - 1 = 2/3x + 4 Check: 1 = 2/3(-6) = check! 1 = 1

y = 1 Part VI #2: (-4,1) and horizontal line x = -3 Part VI #4: (-3,-5) and vertical line

x = 8 Part VI #5: (8,7) and parallel to x = -2 x = 2 Part VI #6: (2,2) and perpendicular to y = 3 All vertical lines are parallel A vertical line is perpendicular to a horizontal line

Homework pg. 555 #1-16 Even #17-33 Odd Reminder to Mr. Willis Print out Test Averages from the year Sometime late do the alg. 2 read. test

Homework HW is evens b/c we did odds w/sub Reminder to Mr. Willis Print out Test Averages from the year Sometime late do the alg. 2 read. test

Given x and y intercepts: 1. x-int: 2 y-int: -3 (2,0) (0,-3) ● ● Notice that the slope is rise 3 run 2 or (2,0) (0,-3) (-3) 2 or y-int x-int. The y intercept (b) of -3 is given The equation in slope intercept form isy = 3 2 x opposite

Given Intercepts Complete exercises #2-3 in Part II and check below. 2. y = 3/4x y = -7/3x - 7 To write the equation in slope-intercept form use the pattern : y = y-intercept x-intercept x + y-intercept slope m b