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Exercises Graphs and straight lines

Example 4.19 from Elementary Algebra, 4.3 Graph with Intercepts

Graph with Intercepts: example 4.19

Find the x- and y- intercepts on each graph.

Three figures, each showing a different straight line on the x y- coordinate plane. The x- axis of the planes runs from negative 7 to 7. The y- axis of the planes runs from negative 7 to 7. Figure a shows a straight line going through the points (negative 6, 5), (negative 4, 4), (negative 2, 3), (0, 2), (2, 1), (4, 0), and (6, negative 1). Figure b shows a straight line going through the points (0, negative 6), (1, negative 3), (2, 0), (3, 3), and (4, 6). Figure c shows a straight line going through the points (negative 6, 1), (negative 5, 0), (negative 4, negative 1), (negative 3, negative 2), (negative 2, negative 3), (negative 1, negative 4), (0, negative 5), and (1, negative 6).

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

1
Solution
1. ⓐ The graph crosses the x- axis at the point $(4, 0)$ . The x- intercept is $(4, 0)$ .
  The graph crosses the y- axis at the point $(0, 2)$ . The y- intercept is $(0, 2)$ .
2. ⓑ The graph crosses the x- axis at the point $(2, 0)$ . The x- intercept is $(2, 0)$
  The graph crosses the y- axis at the point $(0, −6)$ . The y- intercept is $(0, −6)$ .
3. ⓒ The graph crosses the x- axis at the point $(−5, 0)$ . The x- intercept is $(−5, 0)$ .
  The graph crosses the y- axis at the point $(0, −5)$ . The y- intercept is $(0, −5)$ .

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Find the x- and y- intercepts on the graph.

A figure showing a straight line on the x y- coordinate plane. The x- axis of the plane runs from negative 10 to 10. The y- axis of the planes runs from negative 10 to 10. The straight line goes through the points (negative 8, negative 10), (negative 6, negative 8), (negative 4, negative 6), (negative 2, negative 4), (0, negative 2), (2, 0), (4, 2), (6, 4), (8, 6), and (10, 8).

How did it go?

PreviousGraph Linear Equations in Two Variables: example 4.16 Next Graph with Intercepts: example 4.22

From Elementary Algebra (1st edition) by OpenStax (Rice University), section 4.3, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.