# Which of the Following is the Graph of

Which of the Following is the Graph of

## Key points

• In order to work with gradients and direct lines successfully, a proficient understanding of coordinates and linear graphs is needed.

• The

is a measure of slope. The greater the gradient, the steeper the slope.

• When the gradient of 2 lines are the aforementioned, they are

. When the gradients have a

of -1, they are

.

• The slope of a line is calculated by dividing the difference in the

\(y\)
-coordinates past the difference in the

\(x\)
-coordinates. This may exist referred to every bit the change in

\(y\)

divided by the change in

\(x\)
, or the vertical divided past the horizontal.

## Understanding the slope of a straight line

The slope is the corporeality of

movement for each unit of

movement to the right. The greater the slope, the steeper the slope.

• A

positive

left to correct

. A

negative slope

slopes down from

left to right

.

• A slope of 2 and a gradient of -two have the

same steepness

. A gradient of two slopes

upward

from left to right, and a gradient of -2 slopes

downwards

from left to correct.

• Parallel lines have the aforementioned slope.

• Perpendicular lines are sloped in reverse directions. 1 has a positive gradient and the other has a negative gradient. The product of their gradients is -1

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## Working out the slope of a straight line on a graph

To work out the gradient of a straight line:

1. Choose two points on the line.

• Whatever two points will piece of work.
• Whole numbers make the working easier.
2. Draw a triangle showing the horizontal movement to the right and the vertical movement (up or down).

3. Characterization the triangle with the change in the

\(x\)
-coordinate and the modify in the

\(y\)
-coordinate.

4. Piece of work out the value of the modify in the

\(y\)
-coordinate divided by the change in the

\(x\)
-coordinate.

## Finding the slope and intercept

The

of a directly line tin can be written every bit

\(y = mx + c\)

• \(grand\)

• \(c\)

is the

\(y\)

.

To write the equation of a direct line:

2. Discover the

\(y\)
-intercept, the value at which the line crosses the

\(y\)

.
3. Write the equation in the class

\(y = mx + c\)

## Practise working out the gradient of a straight line

### Quiz

Practise working out the gradient of a straight line with this quiz. Yous may need a pen and newspaper to assist you with your answers.

## Real-life maths

The gradient of a line gives the

rate of modify

.

Although graphs in real life may not always exist directly lines, the principle of using gradients equally a rate of change is useful.

Scientists, such every bit physicists, might deport out experiments where they need to rail the distance a

travels over fourth dimension. They could utilise a graph to show this and the slope of the graph would show the speed of the particle.

when calculating the gradient of a roof, otherwise known as the roof βpitchβ.

There are rules and regulations for how steep a roof can be.

For example, if the steepest incline immune for a house extension is 15Β° (this is a gradient of approximately 0Ϋ°268), this will have an bear upon on the distance that the extension can be congenital out to the original walls of the house.

### Which of the Following is the Graph of

Source: https://www.bbc.co.uk/bitesize/topics/zdbc87h/articles/z4ctng8