Math Problem Statement
Solution
Here's a clearer breakdown of the problems from your image:
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Problem 16: If the line through points and is parallel to the line , what is the value of ?
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Problem 17: Solve the equation and then evaluate .
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Problem 18: Solve the equation .
I will now solve each of these problems step by step.
Problem 16: Equation of the Line and Value of
Given that the slope of the line is 3, we find the slope between the points and . The slope formula between these points is:
Setting this equal to 3:
Solving for :
Problem 17: Solving the Equation
Given:
Subtract 7 from both sides:
Multiply both sides by 2:
Divide both sides by 5:
Subtract 4 from both sides:
Now, evaluate :
Problem 18: Solving for
Given:
Simplify the numerator:
Multiply both sides by :
Subtract 9 from both sides:
Divide both sides by :
Simplified, .
If you have any questions about these solutions or need further clarification, please let me know!
Additional Questions to Expand Your Understanding:
- How do you determine the slope between two points on a graph?
- What properties do parallel lines share regarding their slopes?
- How can you solve multi-step equations that involve fractions?
- What are the common mistakes to avoid when solving for variables in equations?
- How can you double-check your solutions for equations?
Tip: Always check if your final answers make sense by substituting them back into the original equations.
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Math Problem Analysis
Mathematical Concepts
Algebra
Slope
Parallel Lines
Formulas
Slope formula m = (y2 - y1) / (x2 - x1)
Theorems
Parallel line slopes are equal
Suitable Grade Level
Grade 9
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