Give the equation of a line that goes through the point \( (-2,-6) \) and is parallel to the line \( -7 x-2 y=-4 \).

Step 1. Find the slope of the given line. The equation provided is –7x – 2y = –4. To find the slope, solve for y:   –2y = 7x – 4   y = (–7/2)x + 2 Thus, the slope of the given line is –7/2. Step 2. Use the point-slope form. Because parallel lines have the same slope, the new line will also have a slope of –7/2 and must pass through (–2, –6). The point-slope form is:   y – y₁ = m (x – x₁) Substituting in the values:   y – (–6) = (–7/2)(x – (–2))   y + 6 = (–7/2)(x + 2) Step 3. Simplify to slope-intercept form. Distribute (–7/2) to (x + 2):   y + 6 = (–7/2)x – 7 Subtract 6 from both sides:   y = (–7/2)x – 7 – 6   y = (–7/2)x – 13 Thus, the equation of the line is:   y = (–7/2)x – 13 Step 4. Alternative standard form (optional). To express in standard form, multiply the entire equation by 2:   2y = –7x – 26 Bring all terms to one side:   7x + 2y = –26 Either form is acceptable as the final answer.