Properties of straight lines
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PROPERTIES OF STRAIGHT LINES
1.Forms of Equation of a Line
2.Slope and its Properties3.Intercepts
TOPIC 7
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Definition:Straight Lines - is the line that does not
change direction.
Slope of a Line -also called as gradient of straight line. It is the measure of the ratio of the vertical change to the horizontal change.x –Intercept - is the point where the graph
of the line crosses the x – axis.
y –Intercept - is the point where the graph of the line crosses the y – axis.
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Forms of Equation of a Line
FORM NAME EXAMPLEax + by + c = 0 General form 2x + 4y + 8 = 0
ax + by = c
y – y1 =m(x – x1)
y =mx + b
Standard form
Point-slope form
Slope-intercept
Intercept form
Two point form
2x + 4y = - 8
y - 4 = -½(x-12)
y = -½x - 2
x y+ =1
b a
1 2 1
1 2 1
y-y y -y= =m
x-x x -x
14 2
x y
1 1
1 1
3-y 4-y 1= =-
10-x 12-x 2
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Lets do these:
1.
Tell what form of equation of a straight line Is being given by each equation.
2.
3.
4.
5.
6.
7.
8.
9.
10.
5x + 10y + 25 = 0
y - 4 = -½(x-6)
-1 y=
2x 5
2x + 4y = -8
17 5
x y
1 1
1 1
6-y 4-y 2= =-
12-x 6-x 3
3x + 9y + 12 = 02
y= 3
x 8
-3x + 6y = 12
3y - 5 = (x-10)
4
General form
Standard form
Point-slope form
Intercept form
Slope-intercept
Two point form
General form
Slope-intercept
Standard form
Point-slope form
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Gradient (Slope) of a Straight Line
Gradient (also called Slope) of a straight line shows how steep a straight line is.
y changegradient
x change
2 1
2 1
y ym
x x
or
Symbol used m=
ris
un
e
r
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Different Types of Gradients ( Slope ) of a Straight Line.
1. A line going up from left to right* rise is positive, and run is positive
4
2Gradient
2m Slope or Gradient ( m ) is positive
rise
runrise
run
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2. A line going down from left to right
* Down is negative , and run is positive
4
2Gradient
2m
Slope or Gradient ( m ) is negative
down
rundown
run
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3. A line that goes straight across
0
5Gradient
0m
Slope or Gradient ( m ) is zero
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4. A line straight up and down
3
0Gradient
m undefined
Slope or Gradient ( m ) is undefined
* Division by zero is not possible.
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Find the gradient(slope) of the linegiven by the graph.
rise
7
run4
Gradient =rise
run
Gradient =
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m = change in y change in x
Gradient =
Gradient =
Find the gradient(slope) of the lineGiven by the graph.
2
1
4
-2
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Find the gradient (slope) of these lines:
a.
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Find the gradient (slope) of these lines:
b.
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Find the gradient (slope) of these lines:
c.
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Find the gradient (slope) of these lines:
d.
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Find the gradient(slope) of the linegiven by points on the graph.
( -1, 8 )
( 7, -1 )
2 1
2 1
y ym
x x
m-1 - 8
=
( x1, y1 )
( x2, y2 )
7 – (-1)
- 9m =
8
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Use the Slope Formula to find the gradient :
a.
m =1
4
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Use the Slope Formula to find the gradient :
b.
m =7
2
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Use the Slope Formula to find the gradient :
c.
m = 6
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Use the Slope Formula to find the gradient :
d.
m = -1
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x – intercept = 0
X - Intercept of a Straight LineThe X - intercept of a straight line is simply where
the line crosses the x - axis.
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Identify the x – intercept of these lines:
a.
x - intercept = none
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Identify the x – intercept of these lines:
b.
x - intercept = 0
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Identify the x – intercept of these lines:
c.
x - intercept = -5
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Identify the x – intercept of these lines:
d.
x - intercept = 5
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Y - Intercept of a Straight LineThe Y intercept of a straight line is simply where
the line crosses the Y axis.
= 1
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Identify the Y-intercept of these lines:
a.
Y- intercept = -2
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Identify the Y-intercept of these lines:
b.
y - intercept = 0
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Identify the Y-intercept of these lines:
c.
y - intercept = none
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Identify the Y-intercept of these lines:
d.
y - intercept = -3