Questions: Consider the following equations. 4-(5y+2x)=6(x-y) and y+7=9+8x Step 1 of 3: Express the first equation in slope-intercept form. Simplify your answer.

Consider the following equations. 4-(5y+2x)=6(x-y) and y+7=9+8x Step 1 of 3: Express the first equation in slope-intercept form. Simplify your answer.
Transcript text: Consider the following equations. \[ 4-(5 y+2 x)=6(x-y) \text { and } y+7=9+8 x \] Step 1 of 3: Express the first equation in slope-intercept form. Simplify your answer.
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Solution

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Solution Steps

To express the first equation in slope-intercept form, we need to isolate \( y \) on one side of the equation. Start by expanding and simplifying the given equation, then solve for \( y \) in terms of \( x \).

Step 1: Expand and Rearrange the Equation

Starting with the equation: \[ 4 - (5y + 2x) = 6(x - y) \] we expand both sides: \[ 4 - 5y - 2x = 6x - 6y \] Rearranging gives: \[ -2x - 5y + 4 = 6x - 6y \]

Step 2: Isolate \( y \)

Next, we move all terms involving \( y \) to one side and all other terms to the opposite side: \[ -5y + 6y = 6x + 2x - 4 \] This simplifies to: \[ y = 8x - 4 \]

Final Answer

The equation in slope-intercept form is: \[ \boxed{y = 8x - 4} \]

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