Which graph represents the equation $y=\frac{1}{3} x+11$?
c.
D.
Answer (1)
The equation y = 3 1 x + 11 is a linear equation with a slope of 3 1 and a y-intercept of 11. Assuming graph D has these characteristics, the answer is D .
Explanation
Understanding the Equation We are given the equation y = 3 1 x + 11 and asked to identify the graph that represents it. This is a linear equation in slope-intercept form, y = m x + b , where m is the slope and b is the y-intercept.
Identifying Slope and Y-intercept From the equation, we can identify the slope as m = 3 1 and the y-intercept as b = 11 . This means the line rises 1 unit for every 3 units it runs to the right, and it crosses the y-axis at the point (0, 11).
Analyzing the Graphs Now, we need to examine the provided graphs (c and D) and determine which one has a slope of 3 1 and a y-intercept of 11. Without the actual graphs, I will make a hypothetical decision. Let's assume graph D has a y-intercept of 11 and a positive slope that appears to be 3 1 .
Conclusion Based on the assumption that graph D has a y-intercept of 11 and a slope of 3 1 , graph D represents the equation y = 3 1 x + 11 .
Examples
Linear equations are used in many real-world scenarios. For example, if you are saving money at a constant rate, the equation representing your savings over time is a linear equation. The slope represents your savings rate, and the y-intercept represents your initial savings. Understanding linear equations helps you predict future savings or plan for expenses.
