A+ » VCE » Further Maths U3 & 4 Master Notes » OA4 Graphs and Relations » FM Gradient

## 1.2 Segment and Step Graphs

### Segment Graphs

• Segment graphs consist of a series of straight-line graphs, creating one continuous line.
• Segment graphs are used to model situations which change at distinct points.
• Each segment can be analysed individually as a straight-line graph.

Example

Above is a segment graph modelling the distance a driver is from their house on a particular trip. We can see the first segment begins at (0,0) and ends at (1,40). We can use these points to find the gradient of the segment, which in this case, tells us the speed (km/hr) which the driver was travelling:

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## 1.1 Straight Line Graphs

### Straight Line Graphs

• Relationships of the form: y=mx+c, where m is the gradient and c is the y-intercept, can be modelled graphically as a straight line.

Example

Above is the graph for the linear relationship: y=-2x+1

### Intercepts

• Two points which are often of interest in graphs are the points at which they cross the x-axis, and where they cross the y-axis. These are known as the x-intercept and y-intercept, respectively.
• To find the x-intercept given a formula, set y to 0 and solve for x.
• To find the y-intercept given a formula, set x to 0 and solve for y.
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