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3-1 Quick Graphs Using Intercepts

This guide explores how to find the x and y intercepts of an equation using graphical and tabular methods. The x-intercept is where a line crosses the x-axis (y = 0), while the y-intercept is where it crosses the y-axis (x = 0). Examples and practice problems are included to help students grasp the concept clearly. For instance, when analyzing equations like 4x + 5y = 40, students will learn to determine intercepts systematically and interpret their meanings in various contexts.

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3-1 Quick Graphs Using Intercepts

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  1. 3-1Quick Graphs Using Intercepts Goal: Find the x and y intercepts of an equation.

  2. Vocabulary • x-intercept – the point that a line crosses the x-axis. (-2, 0) y is always 0 • y-intercept – the point that a line crosses the y-axis. (0, 4) x is always 0

  3. Finding Intercepts of a Graph What are the x and y intercepts of the graph? x-intercept: (4, 0) y-intercept: (0, 200)

  4. Find the x- and y-intercepts of the graphed segment. A. x-intercept is 10; y-intercept is 250 B. x-intercept is 10; y-intercept is 10 C. x-intercept is 250; y-intercept is 10 D. x-intercept is 5; y-intercept is 10

  5. Finding Intercepts of a Table Use the table to determine the x and y intercepts. x-intercept: (500, 0) y-intercept: (0, 2000)

  6. Jules has a gas card for a local gas station. The table shows the function relating the amount of money on the card and the number of times he has stopped to purchase gas.Determine the x- and y-intercepts of the graph of the function. • x-intercept is 5; y-intercept is 125 • x-intercept is 5; y-intercept is 5 • x-intercept is 125; y-intercept is 5 • x-intercept is 5; y-intercept is 10

  7. Describe what the y-intercept of 125 means in the previous problem. • It represents the time when there is no money left on the card. • It represents the number of food stops. • At time 0, or before any food stops, there was $125 on the card. • This cannot be determined.

  8. Finding Intercepts of an Equation • x-intercept – let y = 0 and solve for x • y-intercept – let x = 0 and solve for y • Your answers should be ordered pairs!!! • x-intercepts: (#, 0) • y-intercepts: (0, #)

  9. Find the x and y intercepts of 4x + 5y = 40. x-intercept: y = 0 4x + 5•0 = 40 4x = 40 4 4 x = 10 (10, 0) y-intercept: x = 0 4•0 + 5y = 40 5y = 40 5 5 y = 8 (0, 8)

  10. Examples Find the x and y intercepts: • 2x + 3y = 6 (3, 0) & (0, 2) • - 3.5x + 7y = 14 (-4, 0) & (0, 2) • y = 4x + 40 (-10, 0) & (0, 40) • 4x – 3y = 24 (6, 0) & (0, -8)

  11. Practice • On whiteboards!

  12. Homework • Worksheet – “3-1 Finding Intercepts”

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