Question

Nita graphed the system of equations on the graph below.

y = negative 3 (x + 2). Y = negative 3 x minus 6.

On a coordinate plane, a line goes through (negative 2, 0) and (negative 1, negative 3).

Which explains why there is only one line?
Each has a slope of –3 and a y-intercept of –6, so the system has infinitely many solutions.
Each has a slope of –3 and a y-intercept of –6, so the system has no solution.
Each has a slope of –3, but one has a y-intercept of 2 and the other has a y-intercept of –6. So, the system has infinitely many solutions.
Each has a slope of –3, but one has a y-intercept of 2 and the other has a y-intercept of –6. So, the system has no solution.

Answer 1

To analyze the provided equations, we first need to rewrite them in slope-intercept form (y = mx + b):

1. \( y = -3(x + 2) \) simplifies to:
\[
y = -3x - 6
\]

2. The second equation is already in slope-intercept form:
\( y = -3x - 6 \).

From both equations, we can see that they have the same slope of -3 and the same y-intercept of -6.

Since both equations represent the same line, it means that there are infinitely many solutions (every point on the line is a solution).

So the correct explanation is:
**Each has a slope of –3 and a y-intercept of –6, so the system has infinitely many solutions.**