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Which of the following statements is true about the graph of a linear equation with a positive slope?

Question

Which of the following statements is true about the graph of a linear equation with a positive slope?

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Solution

When considering the graph of a linear equation with a positive slope, it's important to understand the behavior and characteristics of such graphs. Here are some key points regarding this matter:

  1. Direction of the Line: A linear equation with a positive slope will rise from left to right. This means that as the x-value increases, the y-value also increases.

  2. Y-Intercept: The y-intercept can be positive, negative, or zero. However, regardless of its value, the line will always continue to rise as you move to the right.

  3. Quadrants: The graph will occupy parts of the first and third quadrants. If the y-intercept is positive, it will cross the y-axis above the origin, affecting its position.

  4. Linear Relationship: The positive slope indicates a direct (positive) linear relationship between the two variables. This means that for every unit increase in x, there will be a consistent increase in y.

  5. Equation Format: The equation can typically be written in the slope-intercept form y=mx+by = mx + b, where m>0m > 0 signifies a positive slope and bb is the y-intercept.

Based on these observations, the true statement about the graph of a linear equation with a positive slope is that it rises from left to right.

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