Question

105 = 6x + 4y = 12

Explanation:

Convert to slope-intercept form

Using the Slope-Intercept Form knowledge point, we solve the given linear equation \(6x + 4y = 12\) for \(y\):

$$
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$$

Identify key graphing features

Using the Y-intercept and Slope Formula knowledge points, we extract the key features from \(y = -\frac{3}{2}x + 3\):

• The \(y\)-intercept is \((0, 3)\).
• The slope \(m\) is \(-\frac{3}{2}\), meaning down 3 units and right 2 units.

Find a second point

Using the Graphing Linear Equations knowledge point, we apply the slope to find another point on the line starting from \((0, 3)\):

$$ (0 + 2, 3 - 3) = (2, 0) $$

This gives us the \(x\)-intercept at \((2, 0)\).

Plot the line

Using the Graphing Linear Equations knowledge point, we draw a straight line passing through the points \((0, 3)\) and \((2, 0)\).

Answer:

The equation \(6x + 4y = 12\) in slope-intercept form is:

$$y = -\frac{3}{2}x + 3$$

To graph this line:

1. Plot the \(y\)-intercept at \((0, 3)\).
2. Use the slope \(m = -\frac{3}{2}\) to move down 3 units and right 2 units to plot a second point at \((2, 0)\).
3. Draw a straight line passing through both points.