Math Problem Statement

Find the x-intercept and the y-intercept of the line below. Click on 'None' if applicable.

Solution

To find the intercepts from the graph:

(a) x-intercept:

The x-intercept is the point where the line crosses the x-axis (y = 0). From the graph, the line crosses the x-axis at (-2, 0). Therefore, the x-intercept is:

x = -2

(b) y-intercept:

The y-intercept is the point where the line crosses the y-axis (x = 0). From the graph, the line crosses the y-axis at (0, 3). Therefore, the y-intercept is:

y = 3

Let me know if you need further explanation or help!

Related Questions:

  1. How do you calculate intercepts algebraically if the equation of a line is given?
  2. Can a line have no x-intercept or y-intercept? In what cases?
  3. What is the slope of the line in this graph, and how is it related to the intercepts?
  4. How do intercepts help in graphing a line efficiently?
  5. How would you verify intercepts using the slope-intercept form of the equation?

Tip: Always identify the x- and y-intercepts carefully from the graph as they can provide direct information about the equation of the line!

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Intercepts

Formulas

To find the x-intercept: Set y = 0 and solve for x
To find the y-intercept: Set x = 0 and solve for y

Theorems

Definition of intercepts in a Cartesian plane

Suitable Grade Level

Grades 6-8