S3 (3.1) Level 4 Gradient & Straight Line.notebook · Gradient is always represented with the...

S3 (3.1) Level 4 Gradient & Straight Line.notebook April 30, 2018

Daily Practice 11.5.2017

Q1. Multiply out and simplify 3(2x + 4) - x(7 - x)

Q2. Solve the equation 3x + 6 = 2x - 18

Q3. A dress cost £40, it was reduced by 15% in the sale, how much is it now?

Q4. Q5. Write 0.0000916 in standard form

L.I: Today we will be learning about gradient.

Gradient

Where have you come across gradient before?

Gradient

The gradient of a slope is a measure of its steepness.

A positive gradient means that the slope goes up from left to right.

A negative gradient means that the slope goes down from left to

right (on coordinate grids only).

Gradient

Gradient is always represented with the letter "m". It can be written as a simplified fraction or a decimal.

Gradients for straight lines are usually written as a fraction. Remember that with a straight line, the gradient never changes.

horizontal distancem = vertical height

GradientWork out the gradient of the following (simplify where possible):

100m

250m 2m

0.5m

0.45m

1.35m

58mm108mm


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GRADIENTS LINES EQUATIONS v2.exe

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Gradient of a straight line

(a) (b)

(c)

(d)

(e) (f)

(g)

(h)

(i)


(a) (b)

(c)

(d)

(e) (f)

(g)

(h)

(i)


I can define gradient and explain

to someone how it is calculated.

I can calculate the gradient of

slopes of various steepness.

Success? Daily Practice 15.5.2017Q1. Calculate the length of h

Q2. Find 34% of 700

Q3. Round 28252 to 3 significant figures

Q4. 3 x 4 - (-8) ÷ 2 Q5.

25.4cm

h cm

17cm

L.I: Today we will be learning how to calculate the gradient given a diagram or points on a coordinate grid.

S.C: I will be able to work out a formula to calculate the gradient given two points.


B

A

What are the coordinates of A and B?

What is the gradient of line AB?

Question:

By drawing the points on a coordinate grid, find the gradient of PQ where P(-3, 2) and Q = (2, -1)


B (3, 2)

A (1, -1)

How can we find the gradient without counting the squares?

Can we come up with a formula

to represent this?


To find the gradient of a line given two points (x1 , y1) and (x2 , y2)

x2 - x1m = y2 - y1

horizontal distancem = vertical height so

Examples: Find the gradient of the lines joining

(a) A(2, -1) and B(4, -5) (b) P(-3, -2) and Q(0, 4)



Q1. Find the value of a car that was worth £6000 and depreciated in value by 12.5%

Q2. Calculate the diameter of a circle that has a circumference of 10cm

Non-calc. use as π

Q3. Write 0.00003471 in scientific notation

Q4. Q5. Find the value of k if the gradient of the

line joining (2, -3) and (4, k) is 7.

L:I: Today we will be learning about the equation of a line.

The equation of a straight line

Any straight line drawn on a coordinate grid can be identified with an equation.

The equation represents the relationship between the x and y coordinates on the line. E.g. y = x + 3 or y = -x

You can draw a line given its equation and you can write the equation of a line given its drawing.

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For example: The line y = 2x means that every y - coordinate is two times the x coordinate.

x y

Drawing a line given its equation

To draw a line given its equation, you can create a table of values to help you.

x y

Drawing a straight line using its equation

Example:

1. Draw the line y = x + 1

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Example:

2. Draw the line y = 2x -1

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Example:

3. Draw the line y = -3x + 2


Example:

y = -3x + 4 Draw graphs of the following:

(a) y = -3x + 4

(b) y = 0.5x - 2

(c) y = -x + 2

DailyPractice Non‐Calculator 18.5.2017Q1. Multiply out and simplify 3(2x - 1) + 4(x + 9)

Q2. What is the gradient of the line joining (-3, 2) and (4, 5)?

Q3.

Q5. Find the value of 3x2 - 2y when x = -3 and y = 4

Q4. Calculate the length of a cube with volume 64cm3

Today we will be continuing to learn how to draw staright lines given their equations.



Draw the following given their equations

State the gradient and the coordinate where the line crosses the y - axis for each

y = x

y = 5x - 1 y = 0.5x + 2

y = -2x + 1


y = x - 5 y = -x + 3

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2

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5

678

9

10y

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-1

-2-3

-4

-5-6

-7-8


Complete the table of values for each and then draw the lines on a suitable coordinate grid.

1. y = x + 52. y = x - 33. y = -3x + 84. y = -x + 35. y =

x 3 0 -2y 8

x 4 0 -3y

x 4 0 -1y

x 3 0 -2y

x 4 0 -6y

Today we will be learning about the connection between the equation of a line and the gradient and y - intercept.

Equation of a straight line

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State the gradient and y - intercept



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Equation of a Line

State the equation


The equation of a line is written in the form y = mx + c where m represents the gradient and c represents the y - intercept.

y = 2x + 4

Gradient = 2y - intercept = (0, 4)


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Daily Practice 25.5.2017Q1. Solve the equation 3(2x - 1) = 2(x - 4)

Q2. -3 - (-17) + 20% of 50

Q3.

Q4. State the gradient of the line joining (-3, 4) and (2, 0)

Q5. Complete the table of values for the line y = 0.25x + 3

x -4 0 4 8y

Today we will be learning how to state the equation of a line given 2 coordinates.

Homework Online due Wednesday 31.5.2017

missdeely.weebly.com

Interpreting the equation of the line

The gradient and y - intercept can only be read from the equation if it is of the form y = mx + c.

If it is not of this form, then it must be rearranged.

State the gradient and y - intercept of the following lines

(i) y = 2x - 3 (ii) y = -x + 5 (iii) y = 0.25x

(iv) 2y = 10x + 4

Examples:

1. State the equation of the line with gradient 4 that crosses the y - axis at (0, 5)

2. State the equation of the line joining (-4, 5) and (0, -3)

Equation of a straight line given two coordinates Daily Practice 26.5.2017

Q1. Multiply out and simplify 7(3x - 1) - (x - 2) + 7x

Q2.

Q3. State the gradient of the line joining (2, -1) and (3, -2)

Q4. State the gradient and the y - intercept of the line y = 2x - 2


Today we will be continuing to learn how to find the equation of a line.

Homework due Wednesday 31.5.17

Level 4 test 1 coming up

Topics: Tolerance, Volume and Surface Area, Time Management, Statistics & Probability, Straight Line.

Equation of a straight line given two coordinates

State the equations of the lines joining the following:

(a) (0, 1 ) and (3, 4)

(b) (0, -5) and (7, -2)

(c) (5, 0) and (0, 3)

(d) (2, -3) and (0, 4)

(e) (-3, 3) and (0, -4)

(f) (2, -5) and (0, -2)

(g) (3, 0) and (0, -3)

(h) (1, -3) and (0, -10)

**(i) (2, 2) and (3, 5)

Daily Practice 29.5.2017Q1. Evaluate 3x2 + 2xy when x = -3 and y = 4

Q2. 7.45 x 3000

Q3. State the median, quartiles and inter-quartile range for the data set below

-2 5 7 9 15 18 2 31

Q4. State the equation of the line joining (2, 3) and (0, -8)

Today we will be continuing to work out the equation of a line.

Homework due Wednesday!

Equation of a line - Questions in context

Example:

A bath contains 150L of water.

Water is drained from the bath at a steady rate of 30 litres per minute. The graph of the volume, V litres, of water in the bath against the time, t minutes, is shown below.

Write down an equation connecting V and t.

V

t0



Equation of a line - Questions in context Equation of a line - Questions in context



Q1. Calculate the gradient of the line joining (-1, 2) and (0, 3)

Q2. Find the new value of a house that was purchased for

£190 000 and increased in value by 2.5%

Q3. Write 18 out of 25 as a percentage

Q4. Q5. Calculate the volume of a cylinder with diameter 30cm and height 1.2m

L.I: Today we will be continuing to learn how to create an equation given two points or the graph of a line.

Homework due today!



Examples:

1. State the equation of a line that has a gradient of 4 and passes through the point (1, 7)

2. State the equation of the line joining (-2, 3) and (2, 5)

When we have 2 points, both of which aren't the y - intercept. Equation of a straight line

Questions:

Q1. State the equation of the lines below:

(a) m = -3 and passes through (3, 5)

(b) m = 2 and passes through (1, 4)

(c) m = and passes through (10, 8)

Q2. State the equations of the lines passing through the following pairs of points:

(a) A(1, 2) and B(3, 4)


Today we will be learning about the equation of vertical and horizontal lines.

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Vertical and horizontal lines


Vertical lines have an undefined gradient and always have the same x-coordinate. They have an equation of the form x = a.

Horizontal lines have a zero gradient and always have the same y - coordinate. They have an equation of the form y = b.

The x - axis has the equation y = 0

The y - axis has the equation x = 0

Vertical and horizontal lines

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State the equations of the lines below

(a)

(b)

(c)

(d)

(e)

Today we will be learning how to find where a line crosses the x - axis.

Homework due!

x - intercept

We can see that at the y - intercept the x - coordinate is always zero.

Therefore at the x - intercept the y -coordinate is always zero.

Examples: 1. State the coordinate where the line y = 2x - 4 crosses the x - axis.

2. The line y = 3x - 9 crosses the x - axis at (t, 0), what is the value of t?


Q1. State the equation of the line joining (-3, 4) and (2, -7)

Q2. State the total surface area and volume of a cube with sides 3cm

Q3. Write in tolerance notation a bolt which has minimum width 2.5cm and maximum width 2.7cm

Q4. What is the probability of choosing a red Jack from a deck of 52 cards?


Today we will be learning how to sketch a line just using the x and y ‐ intercepts.

x - intercept

Sometimes we can sketch a line just using the x and y intercepts.

Examples:1. Sketch the line y = 3x - 12

2. Sketch the line 2y - x = 4

Daily Practice 5.6.2017Q1. Given a = -5 and b = 8, find the value of 3ab - 2a2

Q2. State the equation of the line joining (-1, 4) and (0, -8)

Q3. Find 14% of 2300

Q4. Write 6 and a half million in scientific notation

Q5. 3.58 x 700

Draw each of the following pairs of lines on a coordinate grid by using

the x ‐ intercepts and y ‐ intercepts.

For each pair, state the point where the lines cross (their point of intersection)

Showing that a point is on a line

If a point is on a line, the equation of the line must work for that point.

Example:

Show that the point (-3, -5) is on the line y = 3x + 4

Attachments

GRADIENTS LINES EQUATIONS v2.exe

Straight Line stuff.ggb

SMART Notebook

geogebra_thumbnail.png

geogebra_javascript.js

function ggbOnInit() {}

geogebra.xml

SMART Notebook

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