Question

Which is the graph of x – y = 1?

A coordinate plane with a line passing through (0, 1) and (1, 0).

A coordinate plane with a line passing through (0, negative 2) and (0, 1).

A coordinate plane with a line passing through (0, negative 1) and (1, 0).

A coordinate plane with a line passing through (negative 1, 0) and (0, negative 1).

Answer 1

To determine which graph represents the equation \(x - y = 1\), we can rearrange it into slope-intercept form \(y = mx + b\):

Starting with:
\[
x - y = 1
\]
We can rearrange it to solve for \(y\):
\[
-y = -x + 1
\]
\[
y = x - 1
\]

This shows that the line has a slope of \(1\) and a y-intercept of \(-1\). Therefore, the line will pass through the point \((0, -1)\).

To find another point on the line, we can evaluate it at \(x = 1\):
\[
y = 1 - 1 = 0
\]
So another point on the line is \((1, 0)\).

Now, we can check the options:
- **A coordinate plane with a line passing through (0, 1) and (1, 0)**: This does not match.
- **A coordinate plane with a line passing through (0, -2) and (0, 1)**: This does not match.
- **A coordinate plane with a line passing through (0, -1) and (1, 0)**: This matches.
- **A coordinate plane with a line passing through (-1, 0) and (0, -1)**: This does not match.

Thus, the correct graph for the equation \(x - y = 1\) is the one that passes through \((0, -1)\) and \((1, 0)\).