A coordinate plane with a horizontal line passing through (negative 4, 4), (0, 4) and (4, 4). A coordinate plane with a line passing through (0, negative 3) and (3, 0).

Question

What is the equation in standard form of the line shown on the graph?

x = 4
y = 4
x + y = 4
x – y = 4

Answer 1

To identify the correct equation based on the description provided:

1. The first line mentioned is a horizontal line that passes through the points (-4, 4), (0, 4), and (4, 4). This implies that the y-coordinate remains constant at 4, and thus the equation of this horizontal line is: \[ y = 4 \]

2. The second line passes through the points (0, -3) and (3, 0). To find the equation of this line, we first calculate the slope (m) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-3)}{3 - 0} = \frac{3}{3} = 1 \]

   Now, we can use the point-slope form of a line \( y - y_1 = m(x - x_1) \). Choosing the point (0, -3): \[ y - (-3) = 1(x - 0) \implies y + 3 = x \implies y = x - 3 \]

   To convert this to standard form \( Ax + By = C \), we rearrange it: \[ -x + y = -3 \] Multiplying through by -1 gives: \[ x - y = 3 \]

Now looking at the available options:

• \( x = 4 \) (not correct, this is a vertical line)
• \( y = 4 \) (this is the horizontal line we identified)
• \( x + y = 4 \) (not correct for either line)
• \( x - y = 4 \) (not correct for the line we derived)

None of the answer choices provided correspond to the equation of the second line we derived, \( x - y = 3 \).

Therefore, the correct answer concerning just the horizontal line is: \[ y = 4 \]

If we are required to relate it to the choices given, the line passing through (0, 4) is explicitly represented as \( y = 4 \). The second line formed is not directly represented in the options provided.