Gradient and y-intercept
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26 February 2025
Gradient and y-intercept
LO: To understand and calculate the
gradient of a line.
To identify the y-intercept
Gradient
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Find the gradient of this line.
3
2
3
2
The gradient of this line is
First we pick two points.
Find the vertical distance
between the points.
Find the horizontal distance
between the points.
Gradient
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Find the gradient of this line.
2
– 5
2
5
The gradient of this line is
–
First we pick two points.
Find the vertical distance
between the points.
Find the horizontal distance
between the points.
Gradient
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Find the gradient of this line.
0
5
0
5
The gradient of this line is
=
0
The gradient of any horizontal
line is 0,since the vertical step
is 0.
First we pick two points.
Find the vertical distance
between the points.
Find the horizontal distance
between the points.
Gradient
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Find the gradient of this line.
0
3
3
0
The gradient of this line is
=
undefined
The gradient of any
vertical line is
undefined
First we pick two points.
Find the vertical distance
between the points.
Find the horizontal distance
between the points.
Gradient
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Draw a line segment with gradient
1
3
1
3
First we plot one point.
Measure the vertical distance
from the numerator
Measure the horizontal
distance from the
denominator
Now we plot the second point.
Draw a line passing through the two points.
The gradient formula
If we want to calculate the gradient of any line.
We need two points on the line.
Find the gradient of this line.
A
B
The gradient of the line AB is
0
x
1
x
2
y
2
y
1
The coordinates of the points.
y
2
–
y
1
x
2
–
x
1
(
x
1
,
y
1
)
(
x
2
,
y
2
)
y
2
–
y
1
x
2
–
x
1
Gradient
(2 , 5)
(4 , 11)
Find the gradient of the line segment joining the points .
(4 , 11)
(2 , 5)
and
= 3
Gradient =
y
2
–
y
1
x
2
–
x
1
y
2
y
1
Gradient =
11
4
x
2
x
1
–
5
–
2
Gradient
(1 , 15)
(4 , 0)
Find the gradient of the line segment joining the points .
(1 , 15)
(4 , 0)
and
= -5
Gradient =
y
2
–
y
1
x
2
–
x
1
y
2
y
1
Gradient =
15
1
x
2
x
1
–
0
–
4
We need one other
point on the graph.
Graph the line with
equation y =
2
x +
3
The other point can
be found by using
the gradient.
y = 2x + 3
3
is the
y intercept
.
X
2
is the
gradient
.
It means:
rise = 2
run = 1
X
Graphing from the gradient-intercept form
rise = 2
run = 1
We need one other
point on the graph.
Graph the line with
equation y =
3
x -
4
The other point can
be found by using
the gradient.
y = 3x - 4
-4
is the
y intercept
.
X
3
is the
gradient
.
It means:
rise = 3
run = 1
X
Graphing from the gradient-intercept form
rise = 3
run = 1
rise = -4
run = 5
We need one other
point on the graph.
Graph the line with
equation y =
-
x +
3
The other point can
be found by using
the gradient.
3
is the
y intercept
.
It means:
X
rise = -4
run = 5
X
Graphing from the gradient-intercept form
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Learn how to calculate the gradient of a line and identify the y-intercept in mathematics. Understand the concept of gradient as a measure of slope and explore the relationship between vertical and horizontal movements. Find out how to apply the gradient formula using two points on a line.
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Presentation Transcript
26 February 2025 Gradient and y-intercept LO: To understand and calculate the gradient of a line. To identify the y-intercept www.mathssupport.org
Gradient The gradient of a line is a measure of how steep the line is. The gradient is a comparison between vertical and horizontal movement. Find the gradient of this line. First we pick two points. 2 Find the vertical distance between the points. 3 Find the horizontal distance between the points. 3 2 The gradient of this line is www.mathssupport.org
Gradient The gradient of a line is a measure of how steep the line is. The gradient is a comparison between vertical and horizontal movement. Find the gradient of this line. First we pick two points. 5 Find the vertical distance between the points. 2 Find the horizontal distance between the points. 2 5 The gradient of this line is www.mathssupport.org
Gradient The gradient of a line is a measure of how steep the line is. The gradient is a comparison between vertical and horizontal movement. Find the gradient of this line. First we pick two points. 5 0 Find the vertical distance between the points. Find the horizontal distance between the points. The gradient of any horizontal line is 0,since the vertical step is 0. 0 5 The gradient of this line is = 0 www.mathssupport.org
Gradient The gradient of a line is a measure of how steep the line is. The gradient is a comparison between vertical and horizontal movement. Find the gradient of this line. First we pick two points. Find the vertical distance between the points. 3 0 Find the horizontal distance between the points. The gradient of any vertical line is undefined 3 0 The gradient of this line is = undefined www.mathssupport.org
Gradient The gradient of a line is a measure of how steep the line is. The gradient is a comparison between vertical and horizontal movement. Draw a line segment with gradient 1 3 First we plot one point. Measure the vertical distance from the numerator 3 1 Measure the horizontal distance from the denominator Now we plot the second point. Draw a line passing through the two points. www.mathssupport.org
The gradient formula If we want to calculate the gradient of any line. We need two points on the line. The coordinates of the points. Find the gradient of this line. x2 x1 y2 (x2, y2) B y2 y1 y1 (x1, y1) A x2 x1 0 y2 y1 x2 x1 The gradient of the line AB is www.mathssupport.org
Find the gradient of the line segment joining the points . (4 , 11) (2 , 5) and 20 15 y2 y1 x2 x1 Gradient = (4 , 11) x2 10 y2 5 2 11 4 5 Gradient = (2 , 5) x1 y1 0 -2 0 2 4 6 -5 6 2= 3 11 5 4 2 Gradient = = www.mathssupport.org
Find the gradient of the line segment joining the points . (1 , 15) (4 , 0) and 20 (1 , 15) x2 y2 y1 x2 x1 15 y2 Gradient = 10 0 4 15 1 Gradient = 5 0 (4 , 0) x1 -2 0 2 4 6 y1 -5 15 3= -5 15 0 1 4 Gradient = = www.mathssupport.org
Graphing from the gradient-intercept form y Graph the line with equation y = 2x + 3 10 9 8 7 3 is the y intercept. run = 1 6 y = 2x + 3 X 5 We need one other point on the graph. The other point can be found by using the gradient. 2is the gradient. rise = 2 4 X 3 y intercept = 3 2 1 x 0 -1 -10 1 2 3 4 5 6 7 9 10 -9 -8 -7 -6 -5 -4 -3 -2 8 -1 -2 -3 -4 -5 -6 It means: rise = 2 -7 -8 run = 1 -9 -10 www.mathssupport.org
Graphing from the gradient-intercept form y Graph the line with equation y = 3x - 4 10 9 8 7 -4 is the y intercept. 6 y = 3x - 4 5 We need one other point on the graph. The other point can be found by using the gradient. 3is the gradient. 4 3 2 1 x 0 -1 -10 1 X 2 3 4 5 6 7 9 10 -9 -8 -7 -6 -5 -4 -3 -2 8 -1 run = 1 rise = 3 -2 -3 X -4 y intercept = -4 -5 -6 It means: rise = 3 -7 -8 run = 1 -9 -10 www.mathssupport.org
Graphing from the gradient-intercept form y Graph the line with equation y = - x + 3 10 4 5 9 8 3 is the y intercept. 7 y intercept = 3 4 5 6 y =- x +3 We need one other point on the graph. The other point can be found by using the gradient. -is the gradient. 5 rise = -4 run = 5 5 4 X 3 rise = -4 2 1 x 0 -1 -10 1 2 3 4 5 6 7 9 10 -9 -8 -7 -6 -5 -4 run = 5 -3 -2 8 -1 X -2 -3 4 -4 -5 -6 It means: -7 -8 -9 -10 www.mathssupport.org
Thank you for using resources from A close up of a cage Description automatically generated For more resources visit our website https://www.mathssupport.org If you have a special request, drop us an email info@mathssupport.org www.mathssupport.org
