please explain question 1---**Extracted Content:** **Question Stem:** Q1 Find the equation for each of these **Sub-questions:** 1) through: (2, 2), parallel to y = x + 4 3) through: (2, -4), parallel to y = 3x + 2 4) thr (Content incomplete in image)

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Let's solve this step by step. We need to find the equation of a line that passes through the point (2, 2) and is parallel to the line y equals x plus 4. Since parallel lines have the same slope, our line will also have slope 1. Using the point-slope form and the given point, we get y minus 2 equals 1 times x minus 2, which simplifies to y equals x. Let's break this down step by step. First, we identify the slope of the given line y equals x plus 4. This line is in slope-intercept form, so the slope is 1. Since parallel lines have the same slope, our new line will also have slope 1. We'll use the point-slope form to find the equation. Now we apply the point-slope form. We substitute m equals 1 and the point (2, 2) into the formula y minus y₁ equals m times x minus x₁. This gives us y minus 2 equals 1 times x minus 2. Simplifying, we get y minus 2 equals x minus 2. Adding 2 to both sides gives us our final answer: y equals x. Let's verify our answer y equals x. First, we check if the point (2, 2) satisfies our equation: substituting x equals 2 gives y equals 2, which matches our point. Second, we verify the slope is 1 by checking that for every 1 unit we move right, we move 1 unit up. Both conditions are satisfied, confirming our answer is correct. Let's solve problem 3 as another example. We need to find the equation of a line through (2, -4) parallel to y equals 3x plus 2. The given line has slope 3, so our parallel line also has slope 3. Using point-slope form with the point (2, -4), we get y plus 4 equals 3 times x minus 2. Simplifying gives us y equals 3x minus 10.