What is the solution with steps---**Question 1 (Partial)**
**Question Stem:**
parallel to m₁
What is the equation of m₂?
**Options:**
A) y = -3x + 16
B) y = -3x + 20
C) y = 2x + 8
D) y = -2x + 13
**Question 2**
**Question Stem:**
Line m₁ has the equation y = √2 + 2x. Line m₂ is parallel to m₁ and passes through the point (6, 9). What is the equation of m₂?
**Options:**
A) y = √3x + 2√3 - 1
B) y = 7 - 2x
C) y = √3x + 2√3
D) y = 2x - 3
**Question 3**
**Question Stem:**
y = 4 + 14x. What is the slope of the question?
**Options:**
A) -4
B) 4
C) 14
D) -14
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Let's examine three questions about linear equations and parallel lines. When lines are parallel, they share the same slope but have different y-intercepts. We'll work through each problem systematically.
Question 1 is incomplete because the equation of line m₁ is not provided. To find a line parallel to m₁, we need to know m₁'s slope first. Since parallel lines have identical slopes, without m₁'s equation, we cannot determine m₂'s equation. This question cannot be solved as stated.
Question 2: Line m₁ has equation y equals square root of 2 plus 2x. Line m₂ is parallel to m₁ and passes through point (6, 9). First, identify m₁'s slope: it's 2. Since parallel lines have the same slope, m₂ also has slope 2. Using point-slope form with point (6, 9): y minus 9 equals 2 times (x minus 6). Simplifying: y equals 2x minus 3. The answer is D.
Question 3: Given y equals 4 plus 14x, what is the slope? First, rearrange to standard slope-intercept form y equals mx plus c. The equation becomes y equals 14x plus 4. In this form, the coefficient of x is the slope. Therefore, the slope is 14. We can visualize this: for every 1 unit we move right, we move 14 units up. The answer is C, 14.
Let's summarize our solutions. Question 1 was incomplete because the equation of line m₁ was missing, making it impossible to solve. Question 2 asked for a line parallel to m₁ with equation y equals square root 2 plus 2x, passing through point (6,9). Since parallel lines have equal slopes, and m₁ has slope 2, we found m₂ has equation y equals 2x minus 3. Question 3 asked for the slope of y equals 4 plus 14x. Rearranging to standard form gives slope 14. Remember: parallel lines always have identical slopes.