What is the slope-intercept form of the linear equation x 4y = 12?

General
1

what is the slope-intercept form of the linear equation x 4y = 12?

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What is the slope-intercept form of the linear equation x 4y = 12?

Answer: To find the slope-intercept form of the linear equation (x - 4y = 12), we need to rearrange it into the form (y = mx + b), where (m) is the slope and (b) is the y-intercept.

Step-by-Step Conversion:

  1. Original Equation: (x - 4y = 12)

  2. Isolate the (y) term:

    • Subtract (x) from both sides to get the term with (y) on its own:
      [
      -4y = -x + 12
      ]

  3. Solve for (y):

    • Divide each term by (-4) to isolate (y):
      [
      y = \frac{-x}{-4} + \frac{12}{-4}
      ]

  4. Simplify:

    • The expression (\frac{-x}{-4}) simplifies to (\frac{x}{4}).
    • The expression (\frac{12}{-4}) simplifies to (-3).

  5. Resulting Equation:
    [
    y = \frac{1}{4}x - 3
    ]

This equation, (y = \frac{1}{4}x - 3), is the slope-intercept form of the given linear equation (x - 4y = 12).

Identifying the Slope and Y-Intercept

  • Slope ((m)): ( \frac{1}{4} )

    • This indicates that for every 1 unit increase in (x), (y) increases by (\frac{1}{4}) units.

  • Y-Intercept ((b)): (-3)

    • This indicates that the line crosses the y-axis at the point ((0, -3)).

Visual Understanding

To better understand the equation’s transformation and characteristics:

  • Graphing:
    • Start by marking the y-intercept at ((0, -3)) on a graph.
    • Use the slope, (\frac{1}{4}), to find another point. From ((0, -3)), move up (1) unit in the y-direction and (4) units in the x-direction to reach the point ((4, -2)).
    • Draw a straight line through these points to represent the equation (y = \frac{1}{4}x - 3).

Summary

The equation (x - 4y = 12) is converted to (y = \frac{1}{4}x - 3) in slope-intercept form. The slope of (\frac{1}{4}) describes the line’s angle relative to the x-axis, and the y-intercept (-3) indicates where the line crosses the y-axis. This format allows for straightforward graphing and analysis of linear relationships. @anonymous6