Sure, let's find the intersection of these two lines.
1. First, we have the equations y = x + 4 and y = 4x - 5.
2. To find the point of intersection, we need to set the two equations equal to each other.
So, x + 4 = 4x - 5.
3. Next, we need to solve for x. We can begin by getting all terms involving x on one side of the equation.
We'll subtract x from both sides, giving us 4 = 3x - 5.
4. To isolate x, add 5 to both sides, which should look like:
9 = 3x.
5. Finally, divide both sides by 3 to solve for x:
x = 3.
6. Now that we know x, we can substitute it into either of the original equations to find y.
We'll use the first one: y = x + 4. Substitute x = 3 into the equation:
y = 3 + 4 = 7.
So, the point of intersection of the lines y = x+4 and y = 4x-5 is (3, 7).