Graphing Lines Review

8/8/2019 Graphing Lines Review

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Understanding Straight Lines

Review


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Graphing Lines

Plotting Points on a Coordinate System

Finding the slope

Graphing a line using points

Graphing a line using intercepts

Graphing a line using slope and a point

Graphing a line using slope and y-intercept

Horizontal & Vertical Lines

Parallel & Perpendicular Lines Equations of a Line

Linear Function Word Problems


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Plotting points on a

coordinate system (x, y)

(0,5)

(6,0)

(-7,3)

(3,-4)


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Positiveslope

Negativeslope

0 slopeUndefinedslope

Types ofstraight lines

slopes


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Finding the slope given

2 points a =

Find the slope of theline connecting

(-2,1) and (6, -3) a = -3 - 1 = -1

6 - (-2) 2

12

12

xx

yy

a


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Graphing a line using points Example:

x y

1 2

-1 63 -2


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Graphing a line using intercepts

Example:2x + y = 4

X-intercept: put 0 infor y and solve for x.

2x + 0 = 4x = 2

(2, 0) is x-intercept

y-intercept: put 0 infor x and solve for y.

2(0) + y = 4

y = 4

(0, 4) is y-intercept

x y0 4

2 0


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Graphing Using the Slope

and a Point Graph the point

Apply the slope (rise

over run) from thatpoint

Connect the points anddraw the line

Example:

Point (1, -2) & a = 1/3


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Graphing line using the slope

and y-intercept Graph y-intercept

Apply slope

(up/down then tothe right)

Draw line

Example:

y-intercept (0, 2)

a = 3/2


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Horizontal & Vertical Lines y = # Horizontal line y-intercept (0, #) Slope is 0 No x-intercept

x= # Vertical line x-intercept is (#, 0)

Slope is undefined No y-intercept


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Parallel & Perpendicular Lines Parallel lines:

have the same slope

Example: y = 2x + 1

y = 2x -4

Both have a slope of2,

therefore the lines areparallel

Perpendicular lines: slopesare negative reciprocals of

each other Example:

y = 3x + 2

y = -1/3 x - 4

First has slope of3 andsecond has a slope of-1/3.

Note: 3 * -1/3 = -1


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2-line relationships: Parallel

Same slope, diff y-int

Coincident Exact same line! (same slope, same y-int)

Perpendicular Flip and change sign of slope, diff y-int

Secant Diff slope, diff y-int


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Types of relations or

variations

Direct

y = x

Partial

y = ax +b

Constant

y = b


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Equations of a Line

y = ax + b (Function form - a is the

slope and b is the y-intercept)

Ax + By + C = 0 (General Form)


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General Form to Functional form

2x 3y 6 = 0

-3y = -2x + 6

y = -2/3 x + 6/3

y = -2/3 + 2


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Functional Form to General Form

y = 4/5 x 8

y 4/5 x + 8 = 0

-4/5 x + y + 8 = 0

-4 x + 4y + 32 = 0

4x 4y 32 = 0

No fractions

Keep order x, y, #

No negatives


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Linear function word problems Independent variable (x)

Dependent variable (y) y = ax + b

InitialvalueRate of

change


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Questions about Lines1. Find the equation of a

line in general form

through (-2, 2) and(1, 3)

2. Find the equation of aline in function formthrough (6, -2) andparallel to 3x - 2y =4

3. Find the equation of a linewith a slope of 0 and a y-

intercept of -3

4. Find the equation of a line

in function form through(4, 3) and perpendicular to2x = 4y + 6


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Answers to Lines1. Find the equation of

a line in general

form through(-2, 2) and (1, 3)

Solution:

Slope = 3 - 2 = 11- (-2) 3

Using y=mx+b:

2 = 1/3 (-2) + b

2 = -2/3 + b

2 + 2/3 = b

8/3 = b

@ y = 1/3 x + 8/3

Answer: 0 = x - 3y + 8


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Answers to Lines2. Find the equation of

a line in function

form through (6, -2)and parallel to3x - 2y = 4

Solution:

Find the slope of 3x - 2y = 4 bysolving for y:

-2y = -3x + 4

y = 3/2 x - 2

m = 3/2 (Parallel lines: same slope)

use y = mx + b- 2 = 3/2 (6) + b

- 2 = 9x + b

- 11= b

@ y = 3/2 x - 11


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Answers to Lines3. Find the equation of a

line with a slope 0 and

a y-intercept of-3

4. Find the equation of aline in function form

through (4, 3) &perpendicular to2x = 4y + 6

Solutions:

Slope of 0 means this is ahorizontal line in the form y = c.@

y = -3 is the answer

Find slope of 2x = 4y + 6 bysolving for y. y = 1/2 x - 3/2

Slope of perpendicular line is -2.

3 = -2 (4) + b

3 + 8 = b

11 = b

@ y = -2x + 11


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Hope you enjoyed straight lines !

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Graphing Lines Review