We are told to write the equation of a line that is parallel to CD. The question gives us the equation for line CD, which is y = -2x - 2 and that the parallel line needs to go through the point (4,5). To start off, we need to find the slope of the line CD, which is y = -2x - 2, or -2. For a line to be parallel to another line, the slope must remain the same.
Next, we use the point-slope formula to find the parallel line's equation. The point-slope form is y - y₁ = m(x - x₁). We plug in -2 for m, 4 for x₁ and 5 for y₁. Doing so gives us y - 5 = -2(x - 4). Now, use the distributive property to simplify. This gives us: y - 5 = -2x + 8. Finally, we add 5 to both sides to get y = -2x + 13. Therefore, the equation of the line parallel to the line CD is y = -2x + 13. Hope this helped and have a phenomenal day!
