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HSC Standard Maths Resources

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10.1 Linear Equations

What is a linear equation? To begin with graphically, anything that produces straight line on a graph has got a linear equation behind it.

All of the following have linear equations behind them:  x and y are the variables that are plotted on x and y axis, m is the gradient and c is the y-intercept. These will become clearer when we look at examples below.

Before looking into examples, note the following formula we will use to work out m and c: Example 1

James sells laptops. If he sells 10 laptops his profit is \$1,300 and when he sells 25 laptops his profit is \$3,550. You are told this follows linear equation. Draw this on a graph. What is the equation of his profit? Are there any limitations?

Example 2

What is the gradient and y-intercept of following linear equations? Example 3 1. What is the y-intercept of blue line?
2. Is gradient of red line positive or negative?
3. Between blue and green line, which one has higher gradient?
4. What is the gradient of yellow line?