Question

graph the solution y < 4x - 3

Answer 1

The best way to think about this is to take the graph in steps. Don't worry about the < symbol at the moment, swap it for an = sign and consider the inequality later.

1: Consider the graph y=x


2: The graph y=4x will be very similar, but for each value of x the corresponding y value will be much greater, so the graph will be much steeper.


3: The graph y=4x-3 will now cut the y=axis at -3, instead of at 0 (the graph is almost 'dropped' down the y-axis 3 steps, and you can work this out as well).
Cuts x-axis, let y=0 in y=4x-3 and solve for x.
Cuts y-axis, let x=0 in y=4x-3 and solve for y.

Based on this, consider y<4x-3. This means the for whatever value of x, we will get a y-value which below the line y=4x-3. This gives an infinitely large region (infinitely many solutions) which from the graph of y=4x-3 you should be able to figure out.