properties of straight lines

PROPERTIES OF STRAIGHT LINES

1.Forms of Equation of a Line

2.Slope and its Properties3.Intercepts

TOPIC 7

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.

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

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

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

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

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

3. A line that goes straight across

0

5Gradient

0m

Slope or Gradient ( m ) is zero

4. A line straight up and down

3

0Gradient

m undefined

Slope or Gradient ( m ) is undefined

* Division by zero is not possible.

Find the gradient(slope) of the linegiven by the graph.

rise

7

run4

Gradient =rise

run

Gradient =

m = change in y change in x

Gradient =

Gradient =

Find the gradient(slope) of the lineGiven by the graph.

2

1

4

-2

Find the gradient (slope) of these lines:

a.

Find the gradient (slope) of these lines:

b.

Find the gradient (slope) of these lines:

c.

Find the gradient (slope) of these lines:

d.

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

Use the Slope Formula to find the gradient :

a.

m =1

4

Use the Slope Formula to find the gradient :

b.

m =7

2

Use the Slope Formula to find the gradient :

c.

m = 6

Use the Slope Formula to find the gradient :

d.

m = -1

x – intercept = 0

X - Intercept of a Straight LineThe X - intercept of a straight line is simply where

the line crosses the x - axis.

Identify the x – intercept of these lines:

a.

x - intercept = none

Identify the x – intercept of these lines:

b.

x - intercept = 0

Identify the x – intercept of these lines:

c.

x - intercept = -5

Identify the x – intercept of these lines:

d.

x - intercept = 5

Y - Intercept of a Straight LineThe Y intercept of a straight line is simply where

the line crosses the Y axis.

= 1

Identify the Y-intercept of these lines:

a.

Y- intercept = -2

Identify the Y-intercept of these lines:

b.

y - intercept = 0

Identify the Y-intercept of these lines:

c.

y - intercept = none

Identify the Y-intercept of these lines:

d.

y - intercept = -3