Question

The graphed line shown below is y = 3 x minus 1.

On a coordinate plane, a line goes through (0, negative 1) and (1, 2).

Which equation, when graphed with the given equation, will form a system that has an infinite number of solutions?
A. y + 1 = 3 x
B. y = negative 3 x + 1
C. y = 3 x + 1
D. y minus 3 x = negative 3

Answer 1

To determine which equation will form a system with an infinite number of solutions when graphed with the given equation \( y = 3x - 1 \), we need to identify an equation that represents the same line.

The given equation is:

\[
y = 3x - 1
\]

Next, let's analyze the options:

A. \( y + 1 = 3x \)

Rearranging this gives:

\[
y = 3x - 1
\]

This is exactly the same as the original equation, so this option will indeed create a system with an infinite number of solutions.

B. \( y = -3x + 1 \)

This line has a different slope (\(-3\)) and will not be the same line, thus it does not produce an infinite number of solutions.

C. \( y = 3x + 1 \)

This line also has the same slope (\(3\)) as the original equation but a different y-intercept (\(-1\) vs \(1\)). So it represents a different line and does not produce an infinite number of solutions.

D. \( y - 3x = -3 \)

Rearranging this gives:

\[
y = 3x - 3
\]

This line again has the same slope (\(3\)) but a different y-intercept (\(-1\) vs \(-3\)), so it represents a different line and does not have infinite solutions.

Thus, the only equation that will yield a system with an infinite number of solutions is option **A**:

\[
\boxed{A}
\]