The Straight Line - Slide
-
Upload
nova-adila-erizal -
Category
Documents
-
view
220 -
download
0
Transcript of The Straight Line - Slide
-
7/30/2019 The Straight Line - Slide
1/53
MATHEMATICS FORM 4
CHAPTER 5 : THE STRAIGHT LINE
SUBTOPIC 5.4 : EQUATION OF A
STRAIGHT LINE
-
7/30/2019 The Straight Line - Slide
2/53
GRADIENT
vertical distancemhorizontal distance
2 1
2 1
m
y y
x x
y interceptm x intercept
-
7/30/2019 The Straight Line - Slide
3/53
vertical distancem
horizontal distance
Vertical distance
horizontal distance
y
x
-
7/30/2019 The Straight Line - Slide
4/53
2 1 1 2
2 1 1 2
y y y ymx x x x
y
x
( x2,y2 )
( x1,y1 )
-
7/30/2019 The Straight Line - Slide
5/53
y interceptmx intercept
y
x
x-intercept
y-intercept
-
7/30/2019 The Straight Line - Slide
6/53
WRITING THE EQUATION OF STRAIGHT LINE
In the equation of straight liney=mx + c, m is the gradient and c isthey-intercept.
Ex:Write equation of straight line, giventhe gradient, m and they-intercept, c.
a) Gradient = 4,y-intercept = 6
b) Gradient = -2,y-intercept = -7
-
7/30/2019 The Straight Line - Slide
7/53
Solution
a) By substitute m= 4 and c = 6 into the
equationy=mx + c
Hence,
The equation of the straight line
y = 4x + 6
-
7/30/2019 The Straight Line - Slide
8/53
Solution..
b) Substitute m= -2, c = -7 into the
equationy=mx + c.
Hence,
The equation of straight line is
y=-2x -7
-
7/30/2019 The Straight Line - Slide
9/53
GRADIENT AND y-INTERCEPT
If the equation of the straight line is given in
the formy=mx + c, then the coefficient ofx,m, is the gradient whereas the constant, c, isthey-intercept.
Ex:
State the gradient andy-intercept of thestraight lines represented by the followingequations.
a) y = 9x -1
b) y = -4x +10
-
7/30/2019 The Straight Line - Slide
10/53
Solution
a) y = 9x
1Compare to they=mx + c where m is gradient
and c isy-intercept.
Hence,Gradient = 9
y-intercept = -1
-
7/30/2019 The Straight Line - Slide
11/53
Solution..
b) y = -4x + 10
Compare to they=mx + c where m is gradient
and c isy-intercept.Hence,
Gradient = -4
y-intercept = 10
-
7/30/2019 The Straight Line - Slide
12/53
If the equation of a straight line in the
form ofpx + qy = r, then we need tochange the subject of the formula toy
so that it is in the form ofy = mx + c.
The gradient andy-intercept can beeasily determined.
-
7/30/2019 The Straight Line - Slide
13/53
Ex:
Determine the gradient and y-intercept
of each of the following straight lines.
a) 6x + 3y = 8
b) -7x + 14y 8 = 0
-
7/30/2019 The Straight Line - Slide
14/53
Solution.
6x + 3y = 8
3y = -6x + 8
y = -2x + 8/3
Hence,
Gradient = -2
y-intercept = 8/3
y = mx + c
-
7/30/2019 The Straight Line - Slide
15/53
b) -7x + 14y 8 = 0
14y = 7x + 8
y = 1/2x + 4/7
Hence,
Gradient = 1/2
y-intercept = 4/7
-
7/30/2019 The Straight Line - Slide
16/53
How to finding the equation of
a straight line
-
7/30/2019 The Straight Line - Slide
17/53
-
7/30/2019 The Straight Line - Slide
18/53
-
7/30/2019 The Straight Line - Slide
19/53
Finding the equation of a
straight line
Straight line which is parallel to
the x-axis.In the figure, the line AB is
parallel to the x-axis
-
7/30/2019 The Straight Line - Slide
20/53
-
7/30/2019 The Straight Line - Slide
21/53
Gradient of line AB,
m
y-intercept of line AB,
c =
By substituting the
values of m and c into
equation y=mx+c Y=
0
03
11
1
1
-
7/30/2019 The Straight Line - Slide
22/53
-
7/30/2019 The Straight Line - Slide
23/53
The equation of the straight lineparallel to the x-axis with the
y-intercept, p
so,y=p
-
7/30/2019 The Straight Line - Slide
24/53
What the equation of straight line PQ?
-
7/30/2019 The Straight Line - Slide
25/53
Answer: y = 3
-
7/30/2019 The Straight Line - Slide
26/53
Straight line which is parallel to
the y-axis
The gradient of a straight line parallel
to the y-axis is undefined as the
horizontal distance between any two
points on the line is always zero
-
7/30/2019 The Straight Line - Slide
27/53
-
7/30/2019 The Straight Line - Slide
28/53
The straight line MN which is
parallel to the y-axis has constantx-coordinate is 4.
Thus , the equation of the straight
line MN isx = 4
-
7/30/2019 The Straight Line - Slide
29/53
The equation of the straightline parallel to the y-axis with
the x- intercept, q
so, x = q
-
7/30/2019 The Straight Line - Slide
30/53
-
7/30/2019 The Straight Line - Slide
31/53
What the equation of straight line RS?
-
7/30/2019 The Straight Line - Slide
32/53
Answer: x = 3
-
7/30/2019 The Straight Line - Slide
33/53
Straight line which passes through a given
point and has a specific gradient
The steps:
1) Substitute the given gradient m, the x-coordinate
and y-coordinate of the point (x,y) intoy = mx + c
2) Solve the equation in step 1 to fine the value ofc
3) Write the equation in the form ofy = mx+c, using
the value ofm and c found in step 2
-
7/30/2019 The Straight Line - Slide
34/53
Example :
Find the equation of the
straight line passing through
the point A(-2,-5) which has agradient of 1/2
-
7/30/2019 The Straight Line - Slide
35/53
Solution
Give that m =1/2, thereforey = 1/2x + cthe point A(-2,-5) satisfied the equation
above.
-5 =1/2(-2) + c
c = -5 + 1
= -4
Thus, the equation of the straight line is
y = 1/2x - 4
-
7/30/2019 The Straight Line - Slide
36/53
Straight line which passes the two
points
Given two point, P ( ) and Q( ),
that lie on a straight line, the equation
of line PQ can be found by followingthe steps in bellow:
11, yx
22, yx
-
7/30/2019 The Straight Line - Slide
37/53
Step 1: Find the gradient of line PQ,
Step 2: Find the value of c (y-intercept)by substituting the value of m
and the coordinates of one ofthe given point (P or Q) into
the equation y = mx + c
Step 3: Substitute the value of m andc into the equation y = mx + c
12
12
xx
yym
-
7/30/2019 The Straight Line - Slide
38/53
Example:
Find the equation of the
straight line passingthrough the point
M(2,-1) and N(4,7)
-
7/30/2019 The Straight Line - Slide
39/53
Solution 1
4
2
8
241)(7m
Gradient of line MN
-
7/30/2019 The Straight Line - Slide
40/53
9)2(41
c
c
cmxy
Substitute m = 4, x = 2 and
y = -1 (coordinates of point M)
Into the equation.
-
7/30/2019 The Straight Line - Slide
41/53
The equation of the line MN
IS y = 4x -9
Substitute m = 4 and c = -9
Into the equation
y = mx + c
-
7/30/2019 The Straight Line - Slide
42/53
Find the equation of the straightline that passes through each pair
of points A(5,2) and B(3,10)
-
7/30/2019 The Straight Line - Slide
43/53
THE GRADIENT
453
210
m
m
-
7/30/2019 The Straight Line - Slide
44/53
What the value of c
22
)5(42
c
c
cmxy
-
7/30/2019 The Straight Line - Slide
45/53
THE EQUATION IS ?
224 xy
-
7/30/2019 The Straight Line - Slide
46/53
FINDING THE POINT OF
INTERSECTION
Complete the table of values and draw the
graphs of the straight line for the equation:
2 14 and 2 2 16y x y x
x 0 1 2 3 4
y 14
2 14y x
10 6 2 -2
-
7/30/2019 The Straight Line - Slide
47/53
x 0 1 2 3 4
y 8
2 2 16y x
109 11 12
-
7/30/2019 The Straight Line - Slide
48/53
The point of intersection of twostraight lines is the only point that
satisfies both equations. The point ofthe intersection of two lines can beobtained by:
a) drawing the graphs of two straightline
b) solving simultaneous equation
-
7/30/2019 The Straight Line - Slide
49/53
CONCLUSION
-
7/30/2019 The Straight Line - Slide
50/53
After verifiedm is a gradient, andc is
the y-interceptcan form the equation of
the straight line.y = mx+c
If the equation of the straight line in the
formax + by + c, transform it intoy = mx+c,then determinethe gradient
andy-intercept
-
7/30/2019 The Straight Line - Slide
51/53
the equation of the straight lineparallel
tothex-axiswith they-intercept,p isy = p
the equation of the straight lineparallel
tothey-axiswith thex-intercept, q is
x = q
The equation of the straight line which passes
-
7/30/2019 The Straight Line - Slide
52/53
The equation of the straight line which passesthrough a give point, (x,y) and has a specificgradient,m.
subtitute m, and (x,y) intoy = mx + cand find the value ofc
by that, form the equation
The equation of the straight line which passes
through two points.find the m
then subtitute m and (x,y) into the
y = mx + c to find cby that, form the equation
-
7/30/2019 The Straight Line - Slide
53/53
To find the point of intersection of two
straight lines:
a) drawing the graphs of two straight line
b) solving simultaneous equation