Question

Find the point of intersection by graphing both lines and observing where they intersect.
Y = -4x + 2
Y = x - 3

Answer 1

To find the point of intersection, we can set the two equations equal to each other and solve for x.

-4x + 2 = x - 3

Adding 4x to both sides, we get:

2 = 5x - 3

Adding 3 to both sides, we get:

5 = 5x

Dividing both sides by 5, we get:

x = 1

Now, substitute this value of x back into either equation to find the corresponding y-value:

Y = x - 3

Y = 1 - 3

Y = -2

Therefore, the point of intersection is (1, -2).

Now, let's graph the two equations to visually verify the point of intersection.

Plotting the points (0, 2) and (1, -2) on a coordinate plane and drawing a straight line through them, we get the graph of the equation Y = -4x + 2.

Similarly, plotting the points (0, -3) and (1, -2) on the coordinate plane and drawing a straight line through them, we get the graph of the equation Y = x - 3.

By observing the intersection of the two lines, we can conclude that the point of intersection is indeed (1, -2).