Math Problem Statement
y = 5x Graph the linear equation in two variables. y = 5x
Solution
To graph the linear equation , follow these steps:
Step 1: Identify the Key Components
- Slope (): The coefficient of is 5, meaning the line rises 5 units for every 1 unit it moves to the right.
- Y-intercept (): Since there is no constant term, the y-intercept is , meaning the line passes through the origin (0,0).
Step 2: Choose Key Points
Select a few values of and compute :
- , then → (-2, -10)
- , then → (-1, -5)
- , then → (0, 0) (y-intercept)
- , then → (1, 5)
- , then → (2, 10)
Step 3: Plot the Points
Plot these points on a coordinate plane.
Step 4: Draw the Line
Connect the points with a straight line extending in both directions.
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Related Questions
- How do you find the slope of a line from an equation?
- What does the graph of look like compared to ?
- How do you determine if a given point is on the line ?
- What happens to the graph if the equation changes to ?
- How do you graph a linear equation using intercepts?
Tip: The slope determines the steepness of the line; a larger absolute value means a steeper line!
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Graphing
Formulas
y = mx + b
Theorems
Slope-Intercept Form Theorem
Suitable Grade Level
Grades 6-8