Find the slope of a line parallel to the line whose equation is 10x+6y=-96 fully simplified 

To find the slope of a line parallel to the line given by the equation \(10x + 6y = -96\), we first need to rewrite the equation in slope-intercept form, \(y = mx + b\), where \(m\) is the slope.

### Step 1: Solve for \(y\)
Starting with the equation:

\[
10x + 6y = -96
\]

First, subtract \(10x\) from both sides:

\[
6y = -10x - 96
\]

### Step 2: Divide by 6
Next, divide every term by 6 to isolate \(y\):

\[
y = \frac{-10x}{6} - \frac{96}{6}
\]

Simplify the fractions:

\[
y = \frac{-5x}{3} - 16
\]

Now, the equation is in slope-intercept form, and the slope is \(m = \frac{-5}{3}\).

### Step 3: Slope of the Parallel Line
The slope of any line parallel to this one will be the same, so the slope of the parallel line is:

\[
\boxed{-\frac{5}{3}}
\]

Do you want further details on this, or have any other questions?

Here are 5 related questions:
1. What is the slope of a line perpendicular to the given line?
2. How would you write the equation of a line parallel to the given line passing through a specific point?
3. Can you convert the slope-intercept form back into standard form?
4. How does changing the constant term in slope-intercept form affect the graph of the line?
5. What does the slope of \(-\frac{5}{3}\) tell you about the steepness of the line?

**Tip:** When dealing with linear equations, converting to slope-intercept form is the easiest way to find the slope!

Find the slope of a line parallel to the line whose equation is 10x + 6y = -96 fully simplified

Learn how to find the slope of a line parallel to the given equation 10x + 6y = -96 by rewriting it in slope-intercept form. This algebraic problem covers linear equations and the concept of parallel lines, suitable for students in Grades 8-10.

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