The equation given is:

\[
-4x - 10y = -7
\]

To simplify this, let's first solve for \( y \) in terms of \( x \). We can rearrange the equation into slope-intercept form (\( y = mx + b \)), where \( m \) is the slope and \( b \) is the y-intercept.

### Step 1: Isolate the \( y \)-term
Add \( 4x \) to both sides of the equation to get:

\[
-10y = 4x - 7
\]

### Step 2: Solve for \( y \)
Now divide both sides by \(-10\) to isolate \( y \):

\[
y = \frac{4x - 7}{-10}
\]

### Step 3: Simplify the equation
Separate the terms on the right-hand side:

\[
y = \frac{4x}{-10} - \frac{7}{-10}
\]

Simplify each term:

\[
y = -\frac{2}{5}x + \frac{7}{10}
\]

So the equation in slope-intercept form is:

\[
y = -\frac{2}{5}x + \frac{7}{10}
\]

This shows that the slope is \(-\frac{2}{5}\) and the y-intercept is \(\frac{7}{10}\).

Do you have any questions or would you like more details?

### Relative Questions:
1. What is the significance of the slope \(-\frac{2}{5}\) in this equation?
2. How would the graph of this equation look?
3. How can we convert this equation into standard form?
4. What happens if you substitute specific values for \(x\) and \(y\)?
5. How can we solve for \(x\) instead of \(y\)?

**Tip:** When solving for one variable, always remember to keep the equation balanced by performing the same operation on both sides.

Explore the step-by-step solution of the linear equation -4x - 10y = -7. This problem covers the concept of slope-intercept form and properties of linear equations. Suitable for students in Grades 8-10.

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