graphing lines review
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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 !
Complete review assignment for marks
Make memory aid
Test on Tuesday
- Tutorials Friday morning(271), Monday morning (201),
Tuesday lunch (271?)
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