To solve the problem, let’s proceed step by step.

We are tasked with writing an equation in slope-intercept form of the line that:

1. Passes through the point $(-6, -2)$,
2. Is parallel to the line $y = -2x + 5$.

Step 1: Understand the slope of the given line.

The given line equation is: $y = -2x + 5$ This equation is in slope-intercept form $y = mx + b$, where $m$ is the slope.

From $y = -2x + 5$, the slope $m$ is -2.

Step 2: Use the slope for the new line.

Since the line we are finding is parallel to the given line, it will have the same slope: $m = -2$

Step 3: Use the point-slope form of a line.

The point-slope form of a line is: $y - y_1 = m(x - x_1)$ where:

• $m = -2$ (the slope),
• $(x_1, y_1) = (-6, -2)$ (the point the line passes through).

Substitute these values: $y - (-2) = -2(x - (-6))$

Simplify: $y + 2 = -2(x + 6)$

Step 4: Simplify to slope-intercept form $y = mx + b$.

Distribute $-2$ on the right-hand side: $y + 2 = -2x - 12$

Subtract $2$ from both sides to isolate $y$: $y = -2x - 14$

Final Answer:

The equation of the line in slope-intercept form is: $y = -2x - 14$

Let me know if you need further clarification or additional examples!

Related Questions:

1. What is the difference between slope-intercept form and point-slope form?
2. How do you determine if two lines are parallel or perpendicular?
3. How can you write the equation of a line given two points?
4. What is the significance of the slope in a linear equation?
5. How do you graph a line using the slope-intercept form?

Tip:

Parallel lines always have the same slope, while perpendicular lines have slopes that are negative reciprocals of each other.