Questions and Answers
What is the x-intercept of the equation x - 2y = 5?
What is the slope of the line represented by the equation x - 2y = 5?
Which point lies on the line represented by the equation x - 2y = 5?
Which of these options shows a line with a slope of 1/2?
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Which point is NOT on the graph of the equation x - 2y = 5?
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Study Notes
Equation and Key Features
- The equation presented is x - 2y = 5.
- The x-intercept occurs when y = 0; solving the equation gives the intercept at (5, 0).
- The slope of the line is 1/2, indicating a gentle upward rise as x increases.
X-Intercept
- The x-intercept at 5 confirms that the line crosses the x-axis at this point, defining a key feature of the line.
Slope Interpretation
- A slope of 1/2 means that for every increase of 1 unit in y, x increases by 2 units.
- Graphically, this leads to a line that is less steep, rising gradually.
Evaluation of Options
- The first option describes a line passing through (0, -2) and (4, 0), which does not match intercept or slope.
- The second option describes a line through (0, 0.5) and (1, -1.5), inconsistent with the x-intercept of 5.
- The third option includes points (-2, 0) and (0, -1), which do not align with the defined x-intercept or slope.
- The fourth option lists points (-3, -4) and (5, 0), with a connection to the x-intercept, indicating a potential match.
Conclusion
- A graph matching the specified criteria must cross at the x-intercept of 5 and exhibit a slope of 1/2. Only the last option correlates with these properties.
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Description
This quiz focuses on understanding key features of the linear equation x - 2y = 5, specifically the x-intercept and slope. You will evaluate different options based on the properties derived from the equation and confirm their correctness against the defined parameters.
