Straight Line Equations Dr J Frost jfrosttiffinkingstonschuk wwwdrfrostmathscom Last modified 30 th August 2015 GCSE specification Understand that an equation of the form y mx c corresponds to a straight line graph ID: 412895
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Slide1
GCSE: Straight Line Equations
Dr J Frost (jfrost@tiffin.kingston.sch.uk)www.drfrostmaths.com
Last modified:
30
th
August 2015Slide2
GCSE specification:
Understand
that an equation of the form y = mx + c corresponds to a straight line graph
Plot straight line graphs from their equations
Plot and draw a graph of an equation in the
form y
= mx + c
Find the gradient of a straight line graph
Find the gradient of a straight line graph from its equation
Understand that a graph of an equation in the form
y
= mx + c has gradient of m and a y intercept of
c (
ie
. crosses the y axis at c)
Understand how the gradient of a real life graph relates to the relationship between the two
variables
Understand how the gradients of parallel lines are related
Understand how the gradients of perpendicular lines are related
Understand that if the gradient of a graph in the form y = mx + c is m, then the gradient of a line perpendicular to it will
be -1/m
Generate equations of a line parallel or perpendicular to a straight line
graphSlide3
x
-5
-
4 -3 -2 -1 0 1 2 3 4 5 6
y
4
3
2
1
-1
-2
-3
-4
What is the equation of this line?
And more importantly, why is it that?
?
□ “Understand
that an equation
corresponds
to a
line graph.”
The line represents all points which satisfies the equation.Slide4
x
-
5
-
4 -3 -2 -1 0 1 2 3 4 5 6
y
4
3
2
1
-1
-2
-3
-4
A
B
C
D
E
F
G
H
Starter
What is the equation of each line?Slide5
Equation of a line
Understand that an equation of the form
corresponds
to a straight line
graph
The equation of a straight line is
gradient
y
-interceptSlide6
Gradient using two points
Given two points on a line, the gradient is:
!
?
?
? Slide7
Gradient from an Equation
Find
the gradient of a straight line graph from its
equation.
Putting in form
:
Gradient is -2
Putting in form
:
Gradient is
?
? Slide8
Test Your Understanding
Find the gradient of the line with equation
.
? Slide9
Exercise 1
Determine the gradient of the lines which go through the following points.
Determine the gradient of the lines with the following equations:
A line
goes through the points
and
. Line
has the equation
. Which has the greater gradient:
So
has greater gradient.
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
1
2
3
a
b
c
d
e
f
g
h
a
b
c
d
e
f
gSlide10
x
-5
-
4 -3 -2 -1 0 1 2 3 4 5 6
y
4
3
2
1
-1
-2
-3
-4
Sketch the line with equation:
□ “
Plot and draw a graph of an equation in the form y = mx +
c”
Drawing Straight Lines
Bro Tip
: To sketch a line, just work out any two points on the line. Then join up. Using
for one point and
for the other makes things easy.
Slide11
x
-5
-
4 -3 -2 -1 0 1 2 3 4 5 6
y
4
3
2
1
-1
-2
-3
-4
Sketch the line with equation:
□ “
Plot and draw a graph of an equation in the form y = mx +
c”
Test Your UnderstandingSlide12
Finding intersection with the axis
Equation
-axis
-axis
Equation
The point where the line crosses the:
?
?
?
?
?
?
When a line crosses the
-axis:
When a line crosses the
-axis:
?
? Slide13
Equation given a gradient and point
The gradient of a line is 3. It goes through the point (4, 10). What is the equation of the line?
Start with
(where
is to be determined)
Substituting:
Therefore
?
The gradient of a line is -2. It goes through the point (5, 10). What is the equation of the line?
? Slide14
Test Your Understanding
Determine the equation of the line which has gradient 5 and goes through the point
.
Determine the equation of the line which has gradient
and goes through the point
.
Find the equation of the line which is parallel to
and goes through the point
?
?
?
1
2
3Slide15
Equation given two points
A straight line goes through the points (3, 6) and (5, 12). Determine the full equation of the line.
(3,6)
(5,12)
Gradient: 3
Equation:
?
?
A straight line goes through the points (5, -2) and (1, 0). Determine the full equation of the line.
(5, -2)
(1,0)
Gradient: -0.5
Equation:
?
? Slide16
Exercise 2
Determine the points where the following lines cross the
and
axis.
Using suitable axis, draw the line with equation
.
A line has gradient 8 and goes through the point
. Determine its equation.
A line has gradient
and goes through the point
. Determine its equation.
Determine the equation of the line parallel to
and goes through the point
.
Determine the equation of the line parallel to
and goes through the point
.
Determine the equation of the lines which go through the following pairs of points:
1
2
3
5
6
4
7
?
?
?
?
?
?
?
?
?
?
?
?
? Slide17
x
-5
-
4 -3 -2 -1 0 1 2 3 4 5 6
y
4
3
2
1
-1
-2
-3
-4
Find the gradients of each pair of perpendicular lines. What do you notice?
m = -2
m = 1/2
m = -1/3
m = 3
?
?
?
?Slide18
Perpendicular Lines
Gradient
Gradient of Perpendicular Line
-4
Gradient
Gradient of Perpendicular Line
-4
?
?
?
?
?
?
If two lines are perpendicular, then the gradient of one is the
negative reciprocal
of the other.
Or:
!Slide19
Example Problems
A line is goes through the point (9,10) and is perpendicular to another line with equation
. What is the equation of the line?
A line
goes through the points
and
. A second line
is perpendicular to
and passes through point B. Where does
cross the x-axis?
Are the following lines parallel, perpendicular, or neither?
Neither. Gradients are
and
. But
, not -1, so not perpendicular.
?
?
?
Q1
Q2
Q3Slide20
Exercise 3
A line
goes through the indicated point and is perpendicular to another line
. Determine the equation of
in each case.
Find the equation of the line which passes through B, and is perpendicular to the line passing through both A and B.
Line
has the equation
. Line
goes through the points
and
. Are the lines parallel, perpendicular, or neither?
so perpendicular.
Determine the equation of the line
.
Known point on
:
So equation of
:
Determine the equation of the line
.
1
2
4
5
?
?
?
?
?
?
?
?
3
? Slide21
GCSE specification:
Understand
that an equation of the form y = mx + c corresponds to a straight line graph
Plot straight line graphs from their equations
Plot and draw a graph of an equation in the
form y
= mx + c
Find the gradient of a straight line graph
Find the gradient of a straight line graph from its equation
Understand that a graph of an equation in the form
y
= mx + c has gradient of m and a y intercept of c (ie. crosses the y axis at c)Understand how the gradient of a real life graph relates to the relationship between the two variablesUnderstand how the gradients of parallel lines are relatedUnderstand how the gradients of perpendicular lines are related
Understand that if the gradient of a graph in the form y = mx + c is m, then the gradient of a line perpendicular to it will be -1/m Generate equations of a line parallel or perpendicular to a straight line
graphSlide22
Two last things…
Midpoint
of two points
Distance
between two points
?
5
4
3
Find
change and
change to form right-angled triangle.
Then use Pythagoras.
?
Just find the average of
and the average of
.
Slide23
Past Exam Questions
See GCSEPastPaper_Solutions.pptx
GCSERevision_StraightLineEquations.docx