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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 graph
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?
𝑥=2?□ “Understand that an equation corresponds to a line graph.”
The line represents all points which satisfies the equation.
x -5 -4 -3 -2 -1 0 1 2 3 4 5 6
y4
3
2
1
-1
-2
-3
-4
A
B
C
D
E
F
G
H
Starter
What is the equation of each line?
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-intercept
Gradient using two points
Given two points on a line, the gradient is:!
(1 ,4 )(3 ,10) 𝑚=3(5 ,7 )(8 ,1) 𝑚=−2
(2 ,2 )(−1 ,10) 𝑚=−83
?
?
?
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 ? ?
Test Your Understanding
Find the gradient of the line with equation .
𝟐 𝒚=𝒙−𝟏?
Exercise 1Determine 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
efgh
abc
d
e
f
g
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.
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 Understanding
Finding intersection with the axis
Equation -axis -axisThe point where the line crosses the:
? ?
? ?
? ?
𝑥
𝑦When a line crosses the -axis:
When a line crosses the -axis:?
?
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?
𝒚=−𝟐 𝒙+𝟐𝟎 ?
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
3
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:
?
?
Exercise 2Determine 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
52
5
𝑥
𝑦
?
?
?
?
?
?
?
?
? ? ? ? ?
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
?
? ?
?
Perpendicular Lines
Gradient Gradient of Perpendicular Line
-4
?
?
?
?
?
?
If two lines are perpendicular, then the gradient of one is the negative reciprocal of the other.
Or:
!
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
Q3
Exercise 3A 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.
𝑥
𝑦
𝑦=−2𝑥+4𝑙
Determine the equation of the line .Known point on :
So equation of :
𝑥
𝑦=3𝑥+5 𝑙
Determine the equation of the line .
1
2
4
5
? ?
? ? ?
?
?
?
3
?
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 graph
Two last things…
Midpoint of two points Distance between two points
(3,6)
(5,9 )
(𝟒 ,𝟕 .𝟓)? (3,6)
(7,9)5
4
3
Find change and change to form right-angled triangle.Then use Pythagoras.
?
Just find the average of and the average of .
Past Exam QuestionsSee GCSEPastPaper_Solutions.pptxGCSERevision_StraightLineEquations.docx
