Question

Graph the equation x-y=6 using the form y = mx + b. (1 point)

Graph one (0,-6) (1,-5)
Graph 2 (0,-4) (1,-10)
Graph 3 (0,0) (6,6)
Graph 4 (0,3) (3,2)

Answer 1

To graph the equation \( x - y = 6 \) in the form \( y = mx + b \), we first need to rearrange the equation into slope-intercept form.

Starting with the equation:

\[
x - y = 6
\]

We can solve for \( y \):

\[
-y = -x + 6
\]

Multiplying through by -1 gives:

\[
y = x - 6
\]

This means that the slope \( m = 1 \) and the y-intercept \( b = -6 \).

Next, we can identify some points based on this equation. For example:

- When \( x = 0 \):
\[
y = 0 - 6 = -6 \quad \text{(Point: (0, -6))}
\]

- When \( x = 1 \):
\[
y = 1 - 6 = -5 \quad \text{(Point: (1, -5))}
\]

With these points (0, -6) and (1, -5), we can now analyze the provided options to find matches:

- **Graph 1** has the points (0, -6) and (1, -5), which perfectly matches our calculations.
- **Graph 2** has (0, -4) and (1, -10), which does not match.
- **Graph 3** has (0, 0) and (6, 6), which does not match.
- **Graph 4** has (0, 3) and (3, 2), which does not match.

Therefore, the correct graph is **Graph 1**: (0, -6) and (1, -5).