Practise the method.Example 1A straight line passes through (4,18) and (7,33). Find its y−intercept.Show worked answerAnswer: −2Gradient =315=5.Substitute a point into y=5x+c to find c=−2.Example 2A machine follows one linear rule. Input 2 gives output 1; input 4 gives 7. Which input gives output 46?Show worked answerAnswer: 17The output rises 6 over two input stepsthe rule is y=3x−5.Solving y=46 gives x=17.Example 3Line L passes through (1,2) and (3,6). A parallel line passes through (1,22). Find the x−coordinate where that parallel line meets y=3x+8.Show worked answerAnswer: 12L has gradient 2;the parallel line has the same gradient.Its given point gives y=2x+20.Equate the two lines: 2x+20=3x+8x=12.