Math Problem Statement

Find the y-intercept and the x-intercept of the line shown in the graph.

Solution

Let's analyze the graph to find the y-intercept and x-intercept of the line.

  1. Y-intercept: The point where the line crosses the y-axis. From the graph, the line crosses the y-axis at y=1y = 1.

  2. X-intercept: The point where the line crosses the x-axis. From the graph, the line crosses the x-axis at approximately x=4x = -4.

Final answers:

  • (a) Y-intercept: y=1y = 1
  • (b) X-intercept: x=4x = -4

Would you like further details or have any other questions?


Here are five follow-up questions you might find interesting:

  1. How can you find the slope of this line using its intercepts?
  2. What is the equation of the line in slope-intercept form?
  3. How does the sign of the slope affect the direction of the line?
  4. What would happen if the y-intercept was at y=0y = 0?
  5. How do you determine intercepts for more complex functions like parabolas?

Tip: The slope of a line can be found using the formula m=y2y1x2x1m = \frac{{y_2 - y_1}}{{x_2 - x_1}} based on two points on the line.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Graphing

Formulas

Y-intercept: Set x = 0, solve for y
X-intercept: Set y = 0, solve for x

Theorems

Intercept Theorem: A line crosses the y-axis when x = 0 and the x-axis when y = 0

Suitable Grade Level

Grades 6-8