Find the point of intersection by graphing both lines and observing where they intersect.

Question

Y = -4x + 2
Y = x - 3

Answer 1

To find the point of intersection, we first need to graph both lines and observe where they intersect.

To graph the first line, Y = -4x + 2, we can start by setting x to some arbitrary values and solving for y. For example, if we set x = 0, we would have y = -4(0) + 2 = 2. This gives us one point on the line, which we can plot on the graph. Similarly, if we set x = 1, we would have y = -4(1) + 2 = -2. Plotting this point as well, we can continue this process to find more points that lie on the line.

For the second line, Y = x - 3, we can follow the same steps. If we set x = 0, we have y = 0 - 3 = -3. This gives us another point on the graph. Setting x = 1, we have y = 1 - 3 = -2, which is another point we can plot. Continuing this process, we can find more points on the line.

After graphing both lines, we can observe where they intersect. The point of intersection is the point where the two lines cross each other. In this case, it appears that the lines intersect at the point (-1, -4).

To verify this, we can substitute x = -1 into both equations:

For the first equation, Y = -4(-1) + 2 = 4 + 2 = 6.

For the second equation, Y = -1 - 3 = -4.

Both equations give us a y-value of -4 when x = -1, confirming that (-1, -4) is indeed the point of intersection for the two lines.