QQuestionMathematics
QuestionMathematics
What is the value of $x$ that will make line $u$ parallel to line $v$ ?
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Answer
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Step 1:I'll solve this step by step using the precise LaTeX formatting guidelines you specified.
Step 2:: Identify the Slope Condition for Parallel Lines
This means the coefficients of $x$ in their equations must be equal.
For two lines to be parallel, they must have the same slope.
Step 3:: Examine the Equations of Lines $u$ and $v$
Line $u$: $$y = 2x + 3
Line $v$: y = mx + 4
Step 4:: Set Up the Slope Equality Condition
2 = m
For these lines to be parallel, their slopes must be equal:
Step 5:: Solve for $x$
2 = x
Therefore:
Final Answer
Key Insights: - Parallel lines have equal slopes - The value of $x$ that makes the lines parallel is 2 - This ensures the coefficient of $x$ is the same in both line equations
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