Math Problem Statement
Find the x-intercept and y-intercept of the given functions and graphs.
Solution
The worksheet asks you to find the x-intercept and y-intercept of several linear functions and graphs. Let’s go over each one step-by-step.
Top Left:
For the graph, observe where the line crosses the x-axis and y-axis:
- x-intercept: This is the point where the line crosses the x-axis. The x-intercept occurs where .
- y-intercept: This is the point where the line crosses the y-axis. The y-intercept occurs where .
Top Right (Graph):
- x-intercept: Looking at the graph, the line crosses the x-axis at .
- y-intercept: The line crosses the y-axis at .
Middle Left:
This is a linear equation in slope-intercept form, , where is the slope and is the y-intercept.
- y-intercept: The y-intercept occurs at , so the y-intercept is .
- x-intercept: To find the x-intercept, set : So the x-intercept is .
Middle Right:
- y-intercept: The y-intercept is , so it’s .
- x-intercept: Set : So the x-intercept is .
Bottom Left:
- y-intercept: The y-intercept is , so it’s .
- x-intercept: Set : So the x-intercept is .
Would you like a further breakdown of any part? Here are five follow-up questions to consider:
- How do you find intercepts for nonlinear functions?
- Can the x-intercept and y-intercept be the same point?
- What is the geometric interpretation of the slope in these functions?
- How do you determine intercepts graphically versus algebraically?
- How would these steps change if the equation were quadratic instead of linear?
Tip: When finding intercepts, always remember that the x-intercept occurs where , and the y-intercept occurs where .
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Math Problem Analysis
Mathematical Concepts
Linear Functions
Intercepts
Graphing
Formulas
y = mx + b (slope-intercept form)
x-intercept: set y = 0
y-intercept: set x = 0
Theorems
-
Suitable Grade Level
Grades 7-10