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