Geometry 13 7 Writing Linear Equations Slope Intercept

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 = -2 x + 5 Complete exercises #1 -3 in Part I and check below. 1. y = 2 x - 1 2. y = -½x + 4 3. y = -2/3 x + 1/3

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

Given Intercepts To write the equation in slope-intercept form use the pattern : y= y-intercept x + y-intercept slope m b Complete exercises #1 -3 in Part II and check below. 1. y = -7/6 x + 7 2. y = 3/4 x + 3 3. y = -7/3 x - 7

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.

Part III #1: Given point and slope. Step 1: Use PS Form • Using (2, 5) and m = 4 (2, 5) Step 2: Simplify to SI Form • (0, -3) y - 5 = 4 x - 8 +5 +5 y = 4 x - 3

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

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

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 = 7 x - 9 3. (-2, -4) and (-3, -1) m = -3 PS: y + 4 = -3(x + 2) or y + 1 = -3(x + 3) SI: y = -3 x - 10

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

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

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 y = x - 11 Check: -2 = 9 - 11 -2 = -2 check!

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

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

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

Homework pg.