Use the graph to a. determine the x-intercepts, if any; b. determine the y-intercepts, if any. For each graph, tick marks along the axes represent one unit each.

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Step 1: Observe the graph and identify the x-intercept. The x-intercept is the point where the graph crosses the x-axis. From the graph, the orange line crosses the x-axis at x = -5. This means the x-intercept is (-5, 0).

Step 2: Observe the graph and identify the y-intercept. The y-intercept is the point where the graph crosses the y-axis. From the graph, the orange line crosses the y-axis at y = 5. This means the y-intercept is (0, 5).

Step 3: Understand the significance of intercepts. The x-intercept represents the value of x when y = 0, and the y-intercept represents the value of y when x = 0. These points are useful for understanding the behavior of the graph.

Step 4: Verify the intercepts by checking the tick marks along the axes. Each tick mark represents one unit, so the x-intercept at (-5, 0) and the y-intercept at (0, 5) are consistent with the graph.

Step 5: Use the intercepts to write the equation of the line if needed. The slope can be calculated using the formula m = (change in y) / (change in x). From the graph, the slope is m = (5 - 0) / (0 - (-5)) = 5/5 = 1. The equation of the line can be written as y = mx + b, where m is the slope and b is the y-intercept.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

X-Intercept

The x-intercept of a graph is the point where the graph crosses the x-axis. At this point, the value of y is zero. To find the x-intercept, you can set the equation of the line to zero and solve for x. In the provided graph, the x-intercept is located at (-5, 0).

Y-Intercept

The y-intercept of a graph is the point where the graph crosses the y-axis. At this point, the value of x is zero. To determine the y-intercept, you set the equation of the line to zero and solve for y. In the given graph, the y-intercept is at (0, 5).

Graph Interpretation

Interpreting a graph involves understanding the relationship between the x and y coordinates represented visually. This includes identifying key features such as intercepts, slopes, and the overall shape of the graph. In this case, recognizing the intercepts helps in analyzing the behavior of the linear function depicted in the graph.