Question

What is the slope of the linear function 10x+2y=6? Use any method of linear functions to solve.
m= ?

Answer 1

To find the slope of the linear function given by the equation \(10x + 2y = 6\), we can rearrange it into the slope-intercept form, which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

Here are the steps to do that:

1. Start with the original equation:
\[
10x + 2y = 6
\]

2. Solve for \(y\) by isolating it on one side of the equation. First, subtract \(10x\) from both sides:
\[
2y = -10x + 6
\]

3. Now, divide every term by 2 to solve for \(y\):
\[
y = -5x + 3
\]

Now the equation is in the slope-intercept form \(y = mx + b\), where:

- The slope \(m\) is \(-5\).
- The y-intercept \(b\) is \(3\).

Therefore, the slope \(m\) of the linear function is:
\[
\boxed{-5}
\]