1. Mathematical Studies for the IB Diploma Second Edition © Hodder & Stoughton Ltd 2012 5.1 Equation of a straight line

2. Mathematical Studies for the IB Diploma Second Edition © Hodder & Stoughton Ltd 2012 Equation of a straight line The graphs below are all of straight lines. All straight lines take the form y = mx + c where ‘m’ and ‘c’ affect the shape and position of the line. The lines are y = x y = 2x + 1 y = ½x – 2 y = –x – 2 y = –3x – 2

3. Mathematical Studies for the IB Diploma Second Edition © Hodder & Stoughton Ltd 2012 Equation of a straight line The effect of m on the shape of a straight-line graph can be seen by plotting several straight-line graphs with different values of m. Therefore in the equation y = mx + c, the value of m represents the gradient of the line. As can be seen from the graphs, the value of m affects the slope (gradient) of the straight line. The bigger the value of m, the steeper the line. If m > 0, the line slopes up to the right. If m < 0, the line slopes up to the left.

4. Mathematical Studies for the IB Diploma Second Edition © Hodder & Stoughton Ltd 2012 Equation of a straight line The effect of c on the shape of a straight-line graph can be seen by plotting several straight-line graphs with different values of c. Therefore in the equation y = mx + c, the value of c represents the y-intercept. As can be seen from the graphs, the value of c affects where the graph intercepts the y-axis.