# 3.3 - Graphs Flashcards

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

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…

(1, 8)

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]

8 euros

I can find the gradient of a straight line

For example, what is the gradient of this line?

[Graph]

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

= -4 ÷ 2

= -0.5

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)?

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

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

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

gradient of the second line is -1 ÷ m

I know what the equation of a line is

y = mx + c

m is the gradient of the line

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

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

y = 6x - 2

What does the line x = 5 look like?

A vertical line passing through (5, 0)

What does the line y = 3 look like?

A horizontal line passing through (3, 0)

What does the line y = x look like?

A diagonal line with gradient 1, passing through (0, 0) and (1, 1)

Goes from bottom left to top right.

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

A diagonal line with gradient -1, passing through (0, 0) and (1, -1)

Goes from top left to bottom right.

Given a formula, I can plot a graph

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

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

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

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

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