Find the point of intersection by graphing both lines and observing where they intersect.
Y = ½ x - 4
Y = -½ x - 1
To graph both lines, we can start by plotting a few points for each equation and then connecting those points to form a line.
For the first equation, Y = ½ x - 4:
- We can choose a few x-values and substitute them into the equation to find the corresponding y-values.
- For x = 0, y = ½(0) - 4 = -4.
- For x = 4, y = ½(4) - 4 = -2.
- For x = -4, y = ½(-4) - 4 = -6.
- Plotting these points (0, -4), (4, -2), (-4, -6), we can connect them to form the line Y = ½ x - 4.
For the second equation, Y = -½ x - 1:
- Similarly, we can choose a few x-values and substitute them into the equation to find the corresponding y-values.
- For x = 0, y = -½(0) - 1 = -1.
- For x = 4, y = -½(4) - 1 = -3.
- For x = -4, y = -½(-4) - 1 = 1.
- Plotting these points (0, -1), (4, -3), (-4, 1), we can connect them to form the line Y = -½ x - 1.
Now, we can observe where the two lines intersect on the graph. The point of intersection is the solution to both equations.
By looking at the graph, we can see that the two lines intersect at the point (2, -3/2).