Math Problem Statement
Solution
Let's solve the given equation step by step to address the questions in the image.
The equation provided is:
1. Determine the intercepts:
To find the x-intercept, set and solve for .
Thus, the x-intercept is .
To find the y-intercept, set and solve for .
Thus, the y-intercept is .
2. Check the other points:
Let’s see if the other points provided satisfy the equation.
-
For :
-
For :
-
For :
Thus, the correct intercept points are (7, 0) and (0, 4), corresponding to the x-intercept and y-intercept.
Summary:
- X-intercept: (7, 0)
- Y-intercept: (0, 4)
Let me know if you need further details! Here are five related questions to deepen your understanding:
- How do you determine the slope of the line from the equation ?
- How would you rewrite in slope-intercept form?
- What is the slope of a line perpendicular to the line described by ?
- If you were to translate the graph of upwards by 2 units, how would the equation change?
- How would you graph the line if the equation were given in standard form , like ?
Tip: When solving for intercepts in linear equations, always set the other variable to 0 to simplify the process.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Intercepts
Formulas
Standard form of a line: Ax + By = C
x-intercept: set y = 0
y-intercept: set x = 0
Theorems
Intercept theorem
Line equation
Suitable Grade Level
Grades 7-9