Question

find the slope and y-intercept that has infinite solutions to the equation
-6x+2y=42
the slope would be -----
the y-interceptwould be-----.

Answer 1

To rewrite the equation \(-6x + 2y = 42\) in slope-intercept form (which is \(y = mx + b\)), we can follow these steps:

1. Start with the equation:
\[
-6x + 2y = 42
\]

2. Solve for \(y\):
\[
2y = 6x + 42
\]
(adding \(6x\) to both sides)

3. Divide every term by 2:
\[
y = 3x + 21
\]

From this equation, we can identify:

- The **slope** (\(m\)) is \(3\).
- The **y-intercept** (\(b\)) is \(21\).

The final answers are:
- The slope would be **3**.
- The y-intercept would be **21**.

Regarding "infinite solutions," this can occur if you have the same linear equation represented in different forms. The slope and y-intercept found here provide one unique line, but if you want infinite solutions, you can express it in the same line form multiple times (like multiplying by a non-zero constant, etc.). In other contexts, "infinite solutions" could refer to two equations that are identical geometrically, which in this case, begins with the same equation being manipulated.