Algebra: X-Intercept and Slope Analysis

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.