Math Problem Statement

y=3x+2

Solution

The equation y=3x+2y = 3x + 2 represents a linear function in slope-intercept form, where:

  • The slope mm is 3, indicating that for every 1 unit increase in xx, yy increases by 3.
  • The y-intercept bb is 2, which is the point where the line crosses the y-axis (at (0,2)(0, 2)).

To analyze further, we can:

  1. Graph the line by plotting two points: the y-intercept at (0,2)(0, 2) and another point by choosing an xx-value, say x=1x = 1, which gives y=3(1)+2=5y = 3(1) + 2 = 5. Plotting these points and drawing a line through them gives a visual of the function.
  2. Interpret the Slope: A slope of 3 means the line is relatively steep, moving up as xx increases.
  3. Calculate Additional Points: Substitute different xx-values to find more points on the line.
  4. Discuss Parallel Lines: Any line with a slope of 3 (e.g., y=3x+cy = 3x + c where c2c \neq 2) would be parallel to this line.
  5. Identify the Line's Equation in Other Forms: Rewrite the equation in point-slope or standard form if needed.

Would you like to dive deeper into any of these aspects? Or perhaps see a graph of this line?

Related Questions

  1. How do you determine the slope and intercept from a linear equation?
  2. What happens to the line if we change the slope to a different value?
  3. How can we identify if two lines are parallel or perpendicular?
  4. What does a negative slope imply about the direction of a line?
  5. How can we rewrite this equation in standard form?

Tip: In linear functions, the slope provides insight into the direction and steepness of the line, which is useful for predicting the behavior of the function as xx changes.

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Math Problem Analysis

Mathematical Concepts

Linear Functions
Slope-Intercept Form
Graphing Linear Equations

Formulas

y = mx + b

Theorems

Slope-Intercept Theorem
Graphing Theorem

Suitable Grade Level

Grades 7-9