Math Problem Statement
Solution
Let's solve each of the parts of the problem given.
Problem Statement
Given the linear equation:
- Find another solution for the equation if is already a solution.
We need to find another pair that satisfies this equation. Let's choose (a simple value) and substitute it into the equation: So, another solution is .
- Check if the points and are solutions to the inequality .
Let's substitute each point into the inequality:
-
For : Since , is not a solution to the inequality.
-
For : Since , is a solution to the inequality.
- Explain how to use the answers to the previous questions to graph the solution set to the inequality.
To graph the solution to the inequality :
- First, graph the line by plotting the points and and drawing a straight line through them.
- Since the inequality is strict (), the line should be dashed to indicate that points on the line are not included in the solution.
- Test a point not on the line (like the origin ). Substituting it into the inequality: Since the origin satisfies the inequality, shade the region of the graph that contains the origin.
Would you like more details on this or have any other questions?
Here are some follow-up questions that might be relevant:
- How do you determine if a point lies on the boundary line of an inequality?
- What would change in the graph if the inequality were instead?
- How do you find the x- and y-intercepts of a linear equation?
- How can you tell if a system of linear equations has no solution, one solution, or infinitely many solutions?
- How does the slope of a line relate to its graphical representation?
Tip: Always check the inequality with a test point after shading to confirm you have the correct region.
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Inequalities
Graphing
Coordinate Geometry
Formulas
2y - 3x = 5
2y - 3x < 5
Theorems
Graphing Linear Equations
Testing Points for Inequalities
Suitable Grade Level
Grades 8-10