5.1.2 Using Intercepts Key Objectives • Find intercepts.
• Graph linear equations using intercepts. • Determine the meaning of intercepts. Key Terms
• The x -intercept is the x -coordinate of the point where a graph crosses the x -axis. • The y -intercept is the y -coordinate of the point where a graph crosses the y -axis.
The graph of every linear function that is not a horizontal line has one x -intercept and one y -intercept. The x -intercept is the x -coordinate of the point where the graph intersects the x -axis. The y-coordinate of this point is always 0. The y-intercept is the y -coordinate of the point where the graph intersects the y -axis. The x -coordinate of this point is always 0. A horizontal line has one y -intercept, and no x -intercepts (except in the case of the horizontal line y = 0, for which every point is an x -intercept). Example 1 Finding Intercepts To find a graph’s x - and y -intercepts, visually identify the points at which the graph intersects the x - and y -axes. The x - and y -intercepts of a function can also be found from its equation. To find the x -intercept, substitute 0 for y and solve for x . To find the y -intercept, substitute 0 for x and solve for y .
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