Math Problem Statement

What is the x-intercept and y-intercept of the graph shown in the image?

Solution

Based on the graph in the image, here are the steps to answer the questions:

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

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

Let me know if you'd like further clarification or if you have any additional questions!


Here are 5 related questions that could expand on this topic:

  1. How do you calculate the slope of a line from its graph?
  2. What is the formula of a line if we know the slope and intercepts?
  3. How do you identify intercepts on graphs of different types of functions?
  4. What is the significance of intercepts in real-world applications like business or science?
  5. How do you graph a line if you are given the slope and one intercept?

Tip: To find intercepts from an equation, set x=0x = 0 for the y-intercept and y=0y = 0 for the x-intercept.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Intercepts
Graphing

Formulas

x-intercept: y = 0
y-intercept: x = 0

Theorems

Intercept theorem

Suitable Grade Level

Grades 7-9