To solve this problem, let's first go step by step:

Step 1: Identify the slope of the line

The equation of the line given is $y = -4x + 2$. This is in slope-intercept form: $y = mx + b$ where:

• $m$ is the slope,
• $b$ is the y-intercept.

From the equation $y = -4x + 2$, the slope $m = -4$.

Since the new line is parallel to this line, it will have the same slope. Therefore, the slope of the new line is also $-4$.

Step 2: Write the equation in point-slope form

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

• $(x_1, y_1)$ is a point on the line, and
• $m$ is the slope.

The problem states that the new line passes through $(-9, -4)$, so $x_1 = -9$ and $y_1 = -4$. Using the slope $m = -4$, the equation in point-slope form becomes: $y - (-4) = -4(x - (-9))$ Simplifying: $y + 4 = -4(x + 9)$

Step 3: Simplify the equation to slope-intercept form

Now, distribute the slope $-4$ on the right-hand side: $y + 4 = -4x - 36$ Subtract 4 from both sides to isolate $y$: $y = -4x - 40$

Final Answer:

• The equation in point-slope form is: $y + 4 = -4(x + 9)$
• The equation in slope-intercept form is: $y = -4x - 40$

Would you like any more details or clarifications?

Here are 5 related questions you can explore:

1. How would the equation change if the line passed through a different point?
2. What happens to the slope if the lines are perpendicular instead of parallel?
3. How do you convert from point-slope form to standard form?
4. How can you find the equation of a line given two points instead of a slope?
5. How does the graph of the line change when the slope increases or decreases?

Tip: Always check the slope when dealing with parallel or perpendicular lines; parallel lines share the same slope, while perpendicular lines have slopes that are negative reciprocals of each other.