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To graph the line with a slope of \(-2\) passing through the point \((-3, 5)\), we can start by finding the equation of the line using the point-slope form:

\[
y - y_1 = m(x - x_1)
\]

where:
- \( m = -2 \) (the slope),
- \((x_1, y_1) = (-3, 5)\) (the point given).

### Step 1: Substitute the values into the equation

\[
y - 5 = -2(x + 3)
\]

### Step 2: Simplify the equation

Expanding the equation:

\[
y - 5 = -2x - 6
\]

Add \(5\) to both sides to solve for \(y\):

\[
y = -2x - 1
\]

### Final Equation
The equation of the line is:
\[
y = -2x - 1
\]

### Graphing the Line
1. Start at the point \((-3, 5)\).
2. Use the slope of \(-2\) (which means "down 2 units for every 1 unit to the right") to find another point on the line.
3. Plot these points and draw a straight line through them.

Would you like me to provide additional details on how to draw this on a coordinate plane, or help with graphing it?

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Here are some related questions:
1. How would you find the equation of a line given two points instead of a point and a slope?
2. What is the significance of the y-intercept in the equation \(y = -2x - 1\)?
3. How do you determine if two lines are parallel by looking at their slopes?
4. How would you find the x-intercept of the line \(y = -2x - 1\)?
5. Can you rewrite \(y = -2x - 1\) in standard form?

**Tip:** Remember, the point-slope form of a line is very useful for quickly finding the equation of a line when you know a point on the line and its slope.

Graph the line with slope -2 passing through the point (-3, 5).

Learn how to graph a line with a slope of -2 that passes through the point (-3, 5). This step-by-step solution demonstrates using the point-slope form to derive the equation y = -2x - 1 and provides tips for accurate graphing.

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