gradient of a line getting ready for a-level€¦ · gradient of a line (1,1) the gradient measures...
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Getting ready for A-Level...Gradient of a line
Getting ready for A-Level Maths...
What you need...– Your brain and attention– A pen and paper– Can do attitude
Gradient of a line
Gradient of a line
(1,1)
Gradient of a line
(1,1)
Gradient of a line
(1,1)
The gradient measures the steepness of a line.
i.e. How far you go vertically for each 1 unit you go to the right.
Gradient
Gradient of a line
(1,1)
The gradient measures the steepness of a line.
i.e. How far you go vertically for each 1 unit you go to the right.
Gradient
Gradient of a line
(1,1)
The gradient measures the steepness of a line.
i.e. How far you go vertically for each 1 unit you go to the right.
Gradient
Gradient of a line
(1,1)
The gradient measures the steepness of a line.
i.e. How far you go vertically for each 1 unit you go to the right.
Gradient
Gradient of a line
(1,1)
The gradient measures the steepness of a line.
i.e. How far you go vertically for each 1 unit you go to the right.
Gradient
Gradient of a line
(1,1)
The gradient measures the steepness of a line.
i.e. How far you go vertically for each 1 unit you go to the right.
Gradient
Gradient of a line
(1,1)
The gradient measures the steepness of a line.
i.e. How far you go vertically for each 1 unit you go to the right.
Gradient
Gradient of a line
(1,1)
The gradient measures the steepness of a line.
i.e. How far you go vertically for each 1 unit you go to the right.
Gradients can be positive, negative, zero, or undefined.
Gradient
Gradient of a line
(1,1)
The gradient measures the steepness of a line.
i.e. How far you go vertically for each 1 unit you go to the right.
Gradients can be positive, negative, zero, or undefined.
Gradient
y2-y1x2-x1
m =
Given two points (x1,y1) and (x2,y2), the gradient between them can be found using the formula:
Formula
change in yGradient=change in x
Gradient of a line
Find the gradient, m, of the line shown on the graph below. Give your answer in its simplest form.
My turn Your turnFind the gradient, m, of the line shown on the graph below. Give your answer in its simplest form.
x
y
x
y
Gradient of a line
Find the gradient, m, of the line shown on the graph below. Give your answer in its simplest form.
My turn Your turnFind the gradient, m, of the line shown on the graph below. Give your answer in its simplest form.
x
y
x
y
Gradient of a line
Find the gradient, m, of the line shown on the graph below. Give your answer in its simplest form.
My turn Your turnFind the gradient, m, of the line shown on the graph below. Give your answer in its simplest form.
x
y
x
y
Gradient of a line
Find the gradient, m, of the line shown on the graph below. Give your answer in its simplest form.
My turn Your turnFind the gradient, m, of the line shown on the graph below. Give your answer in its simplest form.
x
y y
x
Gradient of a line
Find the gradient, m, of the line shown on the graph below. Give your answer in its simplest form.
My turn Your turnFind the gradient, m, of the line shown on the graph below. Give your answer in its simplest form.
x
y y
x
Gradient of a line
Find the gradient, m, of the line shown on the graph below. Give your answer in its simplest form.
My turn Your turnFind the gradient, m, of the line shown on the graph below. Give your answer in its simplest form.
3
6
Ox
y
2
8
Ox
y
Gradient of a line
Find the gradient, m, of the line segments between the points (1,2) and (7,20). Give your answer in its simplest form.
My turn Your turnFind the gradient, m, of the line segments between the points (2,3) and (6,23). Give your answer in its simplest form.
Gradient of a line
Find the gradient, m, of the line segments between the points (1,-8) and (3,-5). Give your answer in its simplest form.
My turn Your turnFind the gradient, m, of the line segments between the points (2,-6) and (5,7). Give your answer in its simplest form.
A(-3,6) and P(a,2a) are two points, where a is a constant. The gradient, m, of AP is 4. Solve for a.
A(-1,3) and P(a,5a) are two points, where a is a constant. The gradient, m, of AP is 7. Solve for a.
Gradient of a lineMy turn Your turnExam Q Exam Q
A(-2,4) and P(a,b) are two points, where a and b are constants. The gradient, m, of AP is 3. Find an expression for b in terms of a.
A(-1,6) and P(a,b) are two points, where a and b are constants. The gradient, m, of AP is 4.
Find an expression for b in terms of a.
Gradient of a lineMy turn Your turnExam Q Exam Q
Gradient of a lineReview Exercise Part 1
2.1.
Find the gradient, m, of the lines shown on the following graphs.Give your answers in their simplest form where appropriate.
3.
x
y y y
x x
Gradient of a lineReview Exercise Part 2
5.4.
Find the gradient, m, of the lines shown on the following graphs.Give your answers in their simplest form where appropriate.
y y
x x
Gradient of a lineReview Exercise Part 3
7.
6.
Find the gradient, m, of the line segments between the points (1,4) and (5,28). Give your answer in its simplest form.
8. Find the gradient, m, of the line segments between the points (2,-9) and (5,-4). Give your answer in its simplest form.
Find the gradient, m, of the line shown on the graph. Give your answer in its simplest form.
4
12
Ox
y
Gradient of a lineReview Exercise Part 1 (Answers)
2.1.
Find the gradient, m, of the lines shown on the following graphs.Give your answers in their simplest form where appropriate.
3.
51m = 4 m = 5 m =
x
y y y
x x
Gradient of a lineReview Exercise Part 2 (Answers)
5.4.
Find the gradient, m, of the lines shown on the following graphs.Give your answers in their simplest form where appropriate.
52m = 3
4m = -
y y
x x
Gradient of a lineReview Exercise Part 3 (Answers)
7.
6.
Find the gradient, m, of the line segments between the points (1,4) and (5,28). Give your answer in its simplest form.
35
8. Find the gradient, m, of the line segments between the points (2,-9) and (5,-4). Give your answer in its simplest form.
Find the gradient, m, of the line shown on the graph. Give your answer in its simplest form.
4
12
Ox
y
m = -3
m = 6
m =