3.6 Parallel Lines in graphing

Slope

Slope intercept form of the line

Slope of the Line

Rise over Run.

The change of

y over the

change in x 11 , yx

22 , yx

12

12

xx

yym

Slope of the Line

Rise over Run.

The change of

y over the

change in x

12

12

xx

yym

2,3

7,4

Using the points (3,2 ) and (4, 7)

Slope is 5

43

72

m

1

5

m

Postulate

Slopes of parallel line are congruent.

These lines are parallel.

The two equations are in what form?

21987

3

287

3

xy

xy

Slope-intercept form of a liney = mx + b

b is for the y intercept ; m is for slope, why m?

I believe (but am not sure) that what we now call just the "slope" was once called the "modulus of slope", the word "modulus" being used in its sense of "number used to measure" (as in "Young's modulus"). John Conway

the first use of the > word (that I know of) back to 1850. Before that phrases such as "the > tangent of the angle between the line and the x-axis" were used. I take > this as evidence that the concept of slope had not crystalized and so name > was attached to it. Both the word "slope" and the use of the letter "m" > seem to have originated in the USA. Fred Rickey

Write the equation of the line

Given Slope : m = 8 and y intercept : b = - 2

Write the equation of the line

Given Slope : m = 8 and y intercept : b = - 2

y = 8x + ( - 2)

y = 8x - 2

Which line through the given points are parallel?

Set of points: (0, - 3) and (1, - 2)

(5, 4) and ( - 4, - 4)

( - 6, - 1) and ( 3, 7)

Which line through the given points are parallel?

Set of points: (0, - 3) and (1, - 2)(5, 4) and ( - 4, - 4)( - 6, - 1) and ( 3, 7)

- 3 – ( - 2) = - 1 = 1 line through (0, - 3) and (1, - 2) 0 – ( 1) - 1 and line through ( - 6, - 1) and ( 3, 7)

4 – ( - 4) = 85 – ( - 4) 9

- 1 – 7 = - 8- 6 – 3 - 9

Which line through the given points are parallel?

Set of points: (0, - 3) and (1, - 2)(5, 4) and ( - 4, - 4)( - 6, - 1) and ( 3, 7)

- 3 – ( - 2) = - 1 line through (5, 4) and (- 4, - 4) 0 – ( 1) - 1 and line through ( - 6, - 1) and ( 3, 7)

4 – ( - 4) = 85 – ( - 4) 9

- 1 – 7 = - 8 = 8- 6 – 3 - 9 9

Point slope form of the line

y – y1 = m(x – x1)

where ( x1 , y1 ) and m are given or need to be found.

Write the equation with m = - 2 and through the point (4, 9)

Point slope form of the line

y – y1 = m(x – x1)

where ( x1 , y1 ) and m are given or need to be found. Write the equation with m = - 2 and through the point (4, 9)

y – 9 = -2( x – 4) Solve for xy – 9 = - 2x + 8y = -2x + 17

Point slope form of the line

y – y1 = m(x – x1)

where ( x1 , y1 ) and m are given or need to be found. Write the equation with m = - 2 and through the point (4, 9)

y – 9 = -2( x – 4) Solve for xy – 9 = - 2x + 8y = -2x + 17

Point slope form of the line

y – y1 = m(x – x1)

where ( x1 , y1 ) and m are given or need to be found. Write the equation with m = - 2 and through the point (4, 9)

y – 9 = -2( x – 4) Solve for xy – 9 = - 2x + 8y = -2x + 17

Point slope form of the line

y – y1 = m(x – x1)

where ( x1 , y1 ) and m are given or need to be found. Write the equation with m = - 2 and through the point (4, 9)

y – 9 = -2( x – 4) Solve for xy – 9 = - 2x + 8y = -2x + 17

Write the equation

Given line k:

Write the equation for line g through ( - 5, 0) and parallel to line k.

35

2 xy

HomeworkHomework

Page 168 – 171Page 168 – 171

##12 – 22 even, 23, 12 – 22 even, 23,

24 – 32 even, 24 – 32 even,

33 – 45 odd, 47, 4833 – 45 odd, 47, 48