In other activities, we have covered solving linear equations using 'algebraic' methods. However, equations can also be solved using a graphical method which is what we consider in this activity.

On this graph we have two straight lines, y = 3x + 1 (in blue) and y = 4 (in red). We can see they meet (or i* ntersect*) at the point (1 , 4). This means that when x = 1 y = 4 and so

**x = 1 is a solution to the equation 3x + 1 = 4.**We can add more horizontal lines to this graph and solve more related equations.

The green line has equation y = -2 and so where it intersects the blue line we have the solution to 3x + 1 = -2. We see that the point of intersection is (-1 , -2) and so* x = -1* is the solution to this equation.

Finally, the purple line has equation y = 8. Where it intersects the blue line we have the solution to the equation 3x + 1 = 8. You will notice this time that the x-value is not a whole number so we must estimate it. It is approximately * x = 2.3* so that is our solution.

Note: we can check this last solution using the 'balancing' method.

3x + 1 = 8

-1 -1

3x = 7

÷3 ÷3

x = 7/3 or 2.33333.....