KS3: Straight Lines Dr J Frost

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KS3: Straight Lines Dr J Frost (jfrosttiffin.kingston.sch.uk) www.drfrostmaths.com Last modified: 14th October 2015 Part 1 Lines and their Equations To print: Yr8StraightLines-Ex1LinesAndTheirEquations x -5 -4 -3 -2 -1 0 1 2 3 4 5 6 y 4 3

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KS3: Straight Lines Dr J Frost (jfrost@tiffin.kingston.sch.uk)
www.drfrostmaths.com Last modified: 14th October 2015

Part 1
Lines and their Equations To print: Yr8StraightLines-Ex1LinesAndTheirEquations

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? ?

L J L J J J L J L ? ? ? ? ? ? ? ? ? On the line?

x -5 -4 -3 -2 -1 0 1 2 3 4 5 6 y 4

3

2

1

-1

-2

-3

-4 ? What and why?

x -5 -4 -3 -2 -1 0 1 2 3 4 5 6 y 8

6

4

2

-2

-4

-6

-8 Exercise 1 - Example If you know the line is a straight line, we can just join them up.

? ? ? ?

x -5 -4 -3 -2 -1 0 1 2 3 4 5 6 y 8

6

4

2

-2

-4

-6

-8

6 1.5 0 ? ? ? Click to Reveal

Put a tick or cross to determine whether each of the following points are on the line with the given equation. ? ? ? ? ? ? ? ?

? ? ? ?

?

Part 1b
Intercepts with the axis

We want to find the coordinates of the points where the line ‘intercepts’ the axes. ? ?

? ? ?

The point where the line crosses the: ? ? ? ? ? ? Copy and complete this table. ? ?

Part 2
Gradient

x -5 -4 -3 -2 -1 0 1 2 3 4 5 6 y 4

3

2

1

-1

-2

-3

-4 ? ? ? ?

! ? Gradient

x -5 -4 -3 -2 -1 0 1 2 3 4 5 6 y 4 3 2 1 -1 -2 -3 -4 On your printed sheet, identify the gradient of each line. A B C D E F G H

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

x -5 -4 -3 -2 -1 0 1 2 3 4 5 6 y 4 3 2 1 -1 -2 -3 -4 Suppose we just had two points on the line and wanted to determine the gradient, but didn’t want to draw a grid. ?

! ? ? ?

Examples Test Your Understanding ? ? ? ? ?

1 2 Determine the gradient of the line which goes through the following points. N1 N2 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

a. Counting Squares b. Using the equation c. Using two points ? ? ?

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 What was the gradient of these lines?

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

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 Now determine the full equation of each line.

?

Copy and complete the following table. ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 1 2 3 4 N ? ? ?

Part 4
Parallel lines

(This was in a Year 8 End of Year exam) ? Preliminary Question: What will be the same about the equations of two lines if they are parallel?
They have the same gradient. ?

?

The gradient of a line is 3. It goes through the point (4, 10). What is the equation of the line? ? The gradient of a line is -2. It goes through the point (5, 10). What is the equation of the line? ? E1 E2

1 2 3 4 ? ? ? N 4 ? ? ? ? ? ? ? ?

A straight line goes through the points (3, 6) and (5, 12). Determine the full equation of the line. (3,6) (5,12) ? A straight line goes through the points (5, -2) and (1, 0). Determine the full equation of the line. (5, -2) (1,0) ? ? Choose one of the two points and then use the previous method we saw when we have a gradient and point. ?

? ?

Work out the gradient given the points on the line. Point 1 Point 2 Full Equation (0,0) (2,2) (-5,0) (0,-5) (1,-3) (3,1) (-4,1) (4, 5) Q1 Q2 Q3 Q4 (-3,7) (2,2) Q5 (1,6) (3,-2) Q6 (-7,3) (5,-1) Q7 (4,9) (-3,10) Q8 ? ? ? ? ? ? ? ? 9 N ? ? ?

REVISION

Vote with your diaries!

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 full equation of a line which has gradient 3 and passes through the point (2,5)?

KS3: Straight Lines Dr J Frost

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