# 3.3 - Graphs Flashcards

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1
Q

I can plot points (x, y) in any of the four quadrants of a graph

A
2
Q

I can workout the midpoint of a line segment, given its endpoints
For example, if a line segment goes from (5, 10) to (-3, 6), its midpoint is…

A

(1, 8)

3
Q

I can read a straight line graph to convert between two units
For example, given the following graph, how many Euros is 7 pounds?
[Graph]

A

8 euros

4
Q

I can find the gradient of a straight line
For example, what is the gradient of this line?
[Graph]

A

gradient = (increase in y) ÷ (increase in x)
= -4 ÷ 2
= -0.5

5
Q

I can find the gradient of a straight line given the coordinates of two points
For example, what is the equation of the straight line through (1, 7) and (2, 9)?

A

gradient = (increase in y) ÷ (increase in x)
= 2 ÷ 1
= 2

```calculate the intercept by substituting into y = mx + c
y = mx + c
7 = 2 × 1 + c
7 = 2 + c
c = 5```

Equation of the line: y = 2x + 5

Given one line, I can find the gradient of another parallel line

6
Q

Given one line, I can find the gradient of another perpendicular line

A

If the gradient of the first line is m, then the

gradient of the second line is -1 ÷ m

7
Q

I know what the equation of a line is

A

y = mx + c

m is the gradient of the line

c is the point where the line crosses the y-axis.

8
Q

What is the equation of the straight line with gradient 6 that passes through the point (0, 2)?

A

y = 6x - 2

9
Q

What does the line x = 5 look like?

A

A vertical line passing through (5, 0)

10
Q

What does the line y = 3 look like?

A

A horizontal line passing through (3, 0)

11
Q

What does the line y = x look like?

A

A diagonal line with gradient 1, passing through (0, 0) and (1, 1)
Goes from bottom left to top right.

12
Q

What does the line y - x = 0 look like?

A

A diagonal line with gradient -1, passing through (0, 0) and (1, -1)
Goes from top left to bottom right.

13
Q

Given a formula, I can plot a graph

A

Draw out a results table for different values of y:
y | 0 | 1 | 2 | 3 | …
x | 2 | 4 | 8 | 16 | …

Plot the points on a graph, and join up with a curve

14
Q

Given a graph of y = f(x), I can sketch y = f(2x)

A

It will be squashed in the horizontal direction, so each point is half as far from the y-axis

15
Q

Given a graph of y = f(x), I can sketch y = 2f(x)

A

It will be stretched out in the vertical direction, so each point is twice as far from the x-axis

16
Q

Given a graph of y = f(x), I can sketch y = 2 + f(x)

A

It will be shifted two up

17
Q

Given a graph of y = f(x), I can sketch y = f(x + 2)

A

It will be shifted two to the left

18
Q

I can estimate the gradient of a non-linear graph

A

Draw a tangent at the point you are interested in (with a ruler)
Calculate the gradient of the tangent like any other straight line

19
Q

I can look at the intersections of lines to solve complex equations
For example, this is a graph of y = x + 4/x - 3
How would you use it to solve the equation 5x + 4/x - 3 = 0?

A
• Rearrange the equation so that it contains the equation of the graph:

0 = 3x + 4/x + 13
0 = ( x + 4/x - 3) + 2x - 10

Substitute in y and rearrange to put y on the left

0 = ( x + 4/x - 3) + 2x - 10
0 = y + 2x - 10
y = -2x + 10

• Draw this new line
• The x-coordinates where the two lines intersect show the solutions