Write the equation in slope-intercept form of a line that passes through the given point and

is parallel to the graph of the given equation.

(−4, −8); 𝑦 = −6𝑥 − 7

To find the equation of the line in slope-intercept form \( y = mx + b \) that passes through the point \((-4, -8)\) and is parallel to the line given by \( y = -6x - 7 \), follow these steps:

### Step 1: Identify the slope of the given line
The slope-intercept form of a line is \( y = mx + b \), where \( m \) is the slope. The slope of the given equation \( y = -6x - 7 \) is \( m = -6 \).

Since the new line is **parallel** to this line, it will have the same slope. Thus, the slope of the new line is also \( -6 \).

### Step 2: Use the point-slope form to find the equation
We can use the point-slope form of the equation of a line, which is:
\[
y - y_1 = m(x - x_1)
\]
Where \( m \) is the slope, and \( (x_1, y_1) \) is the given point. Substituting \( m = -6 \) and \( (x_1, y_1) = (-4, -8) \), we get:
\[
y - (-8) = -6(x - (-4))
\]
This simplifies to:
\[
y + 8 = -6(x + 4)
\]

### Step 3: Simplify to slope-intercept form
Now, simplify the equation to put it in the form \( y = mx + b \):
\[
y + 8 = -6x - 24
\]
Subtract 8 from both sides:
\[
y = -6x - 24 - 8
\]
\[
y = -6x - 32
\]

### Final Equation:
The equation of the line in slope-intercept form is:
\[
y = -6x - 32
\]

Would you like further details or have any questions?

Here are 5 related questions to explore:
1. How do you find the slope of a line from two points?
2. What happens when two lines are perpendicular instead of parallel?
3. How would the equation change if the line passed through a different point?
4. How do you convert from point-slope form to slope-intercept form?
5. How do you determine the y-intercept of a line?

**Tip:** When two lines are parallel, they always have the same slope, no matter their y-intercepts.

Write the equation in slope-intercept form of a line that passes through the given point and is parallel to the graph of the given equation. (−4, −8); 𝑦 = −6𝑥 − 7

Learn how to find the equation of a line in slope-intercept form that is parallel to y = -6x - 7 and passes through the point (-4, -8). This problem involves key algebraic concepts like slope-intercept form and parallel lines theorem, suitable for Grades 8-10 students.

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