Question

Which system of equations is graphed below?

On a coordinate plane, a line goes through (0, 1) and (4, negative 2) and another goes through (0, negative 6) and (6, 0).
x minus y = 6. 4 x + 3 y = 1.
x minus y = 6. 3 x + 4 y = 4.
x + y = 6. 4 x minus 3 y = 3.
x + y = 6. 3 x minus 4 y = 4.

Answer 1

To determine which system of equations is graphed, we first need to find the equations of both lines represented in the graph based on the given points.

### Finding the equation of the first line:
The first line goes through the points (0, 1) and (4, -2).

1. **Calculate the slope (m)**:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - 1}{4 - 0} = \frac{-3}{4}
\]

2. **Use the point-slope form to find the equation**:
Using the point (0, 1):
\[
y - 1 = -\frac{3}{4}(x - 0) \implies y = -\frac{3}{4}x + 1
\]

Rewriting in standard form:
\[
3x + 4y = 4
\]

### Finding the equation of the second line:
The second line goes through the points (0, -6) and (6, 0).

1. **Calculate the slope (m)**:
\[
m = \frac{0 - (-6)}{6 - 0} = \frac{6}{6} = 1
\]

2. **Use the point-slope form to find the equation**:
Using the point (0, -6):
\[
y + 6 = 1(x - 0) \implies y = x - 6
\]

Rewriting in standard form:
\[
x - y = 6
\]

### Therefore, the system of equations:
1. \( x - y = 6 \)
2. \( 3x + 4y = 4 \)

Now, looking at the options given, the correct system of equations is:

**x - y = 6. 3x + 4y = 4.**