In Exercises 6–8, use the graph and determine the x-intercepts if any, and the y-intercepts if any. For each graph, tick marks along the axes represent one unit each.

Verified step by step guidance

1. Observe the graph and identify the points where the line crosses the x-axis and y-axis. These are the x-intercept and y-intercept, respectively.
2. To find the x-intercept, locate the point where the line crosses the x-axis. At this point, the y-coordinate is 0. From the graph, the x-intercept appears to be at x = -2.
3. To find the y-intercept, locate the point where the line crosses the y-axis. At this point, the x-coordinate is 0. From the graph, the y-intercept appears to be at y = 7.
4. Verify the intercepts by checking the coordinates of the points visually on the graph. The x-intercept is (-2, 0), and the y-intercept is (0, 7).
5. Summarize the intercepts: The x-intercept is at (-2, 0), and the y-intercept is at (0, 7). These points represent where the line crosses the respective axes.

Key Concepts

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 context of the provided graph, identifying the x-intercept involves locating the point where the orange line intersects the x-axis.

Y-Intercept

The y-intercept of a graph is the point where the graph crosses the y-axis, where 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 can be found by observing where the orange line intersects the y-axis.

Graph Interpretation

Graph interpretation involves analyzing the visual representation of mathematical functions to extract information such as intercepts, slopes, and trends. Understanding how to read a graph is crucial for solving problems related to linear equations, as it allows you to identify key features like intercepts and the overall behavior of the function represented by the graph.