Questions: Determine the slope of the equation 4x + 1/2 y = -6

Determine the slope of the equation 4x + 1/2 y = -6
Transcript text: Determine the slope of the equation $4 x+\frac{1}{2} y=-6$
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Solution

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Solution Steps

Step 1: Rewrite the Equation

Start with the given equation: \[ 4x + \frac{1}{2}y = -6 \]

Step 2: Isolate \(y\)

To isolate \(y\), subtract \(4x\) from both sides: \[ \frac{1}{2}y = -4x - 6 \]

Step 3: Eliminate the Fraction

Multiply both sides of the equation by \(2\) to eliminate the fraction: \[ y = -8x - 12 \]

Step 4: Identify the Slope

The equation is now in the slope-intercept form \(y = mx + b\), where \(m\) is the slope. From the equation: \[ y = -8x - 12 \] we can see that the slope \(m\) is: \[ m = -8 \]

Final Answer

\(\boxed{-8}\)

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