Find a point on the line and the line's slope.
y+2=-4(x+3)

To find a point on the line and the slope of the line, let’s start by rewriting the equation in slope-intercept form, \( y = mx + b \), where \( m \) is the slope.

Given equation:
\[
y + 2 = -4(x + 3)
\]

### Step 1: Expand and simplify
Distribute \(-4\) on the right side:
\[
y + 2 = -4x - 12
\]

### Step 2: Isolate \( y \)
Subtract \(2\) from both sides:
\[
y = -4x - 14
\]

### Step 3: Identify the slope and a point
In the slope-intercept form \( y = mx + b \):
- The slope \( m \) is \(-4\).
- To find a point on the line, we can use the original form of the equation, where it indicates \((x, y) = (-3, -2)\).

So:
- **Slope**: \(-4\)
- **Point on the line**: \((-3, -2)\)

Would you like further details or have any questions?

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Here are 5 related questions that build on this:

1. How can we verify if another point lies on this line?
2. How would you write the equation of a line parallel to this one?
3. What would be the equation of a line perpendicular to this line?
4. How does changing the slope affect the angle of the line?
5. How would you find the y-intercept from an equation in point-slope form?

**Tip:** To convert equations into slope-intercept form, isolate \( y \) to make it easy to identify the slope and y-intercept.

Find a point on the line and the line's slope. y+2=-4(x+3)

Learn how to find the slope and a point on the line for the equation y + 2 = -4(x + 3). This step-by-step solution covers algebraic concepts, including converting to slope-intercept form and identifying the slope. Suitable for students in Grades 8-10.

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