Solve for the coordinates where lines A and B intersect. A: y=x+4 B: y=0.5x+3.5
The point of intersection is a point where the variables y and x will be the same in both A and B equations. This is because the point of intersection has the same coordinates for both lines. So YA = YB and so x + 4 = 0.5x + 3.5.
Given that x + 4 = 0.5x + 3.5: subtract 0.5x from both sides of the equation, x + 4 - 0.5x = 0.5x + 3.5 - 0.5x.
New equation: 0.5x + 4 = 3.5, We now have the x variable on one side only, making the equation easier to solve.
Now manipulate the equation in a way to get the variables and non-variables on opposing sides (subtract 4): 0.5x + 4 - 4 = 3.5 - 4.
New equation: 0.5x = -0.5
Final step to solve for x: Because x is being multiplied by 1/2 on the LHS and we need x to be multiplied by 1 to get it on its own, we need to multiply the LHS by 2: 0.5x * 2 = -0.5 * 2
New equation: x = -1.
Now we know what x equals, we can substitute the -1 back into the original line equations (choose A or B) to find y.
into A: y = (-1) + 4 so y = 3.
To finish, we have found x and y and so have found the point at which the two lines intersect.
X = -1, Y = 3 OR (-1,3)
