Question

draw the following lines on the same corrdinate plabne and find the coordinates of trhe point of their intersection.
y=1-2x and y=x-5

Answer 1

To find the intersection of the two lines given by the equations \( y = 1 - 2x \) and \( y = x - 5 \), we can set the right-hand sides of the equations equal to each other since both expressions equal \( y \):

\[
1 - 2x = x - 5
\]

Now, let's solve for \( x \):

1. Add \( 2x \) to both sides:
\[
1 = 3x - 5
\]

2. Add \( 5 \) to both sides:
\[
6 = 3x
\]

3. Divide both sides by \( 3 \):
\[
x = 2
\]

Now that we have \( x = 2 \), we can substitute this value back into either equation to find the corresponding \( y \)-coordinate. We'll use the first equation:

\[
y = 1 - 2(2) = 1 - 4 = -3
\]

So, the point of intersection is \( (2, -3) \).

To summarize:
- The coordinates of the intersection point are \( (2, -3) \).

### To Draw the Lines:

1. **For \( y = 1 - 2x \)**:
- If \( x = 0 \), then \( y = 1 \) (point: (0, 1))
- If \( x = 1 \), then \( y = -1 \) (point: (1, -1))
- If \( x = -1 \), then \( y = 3 \) (point: (-1, 3))

2. **For \( y = x - 5 \)**:
- If \( x = 0 \), then \( y = -5 \) (point: (0, -5))
- If \( x = 5 \), then \( y = 0 \) (point: (5, 0))
- If \( x = 1 \), then \( y = -4 \) (point: (1, -4))

By plotting these points on a coordinate plane, you would draw the two lines and see that they intersect at the point \( (2, -3) \).