Thread (2 posts)

Solving the equation $4x + 2y = 12$

Here are two standard approaches:

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1. Slope-intercept form (solving for $y$):

$$\begin{align*} 4x + 2y &= 12 \\ 2y &= -4x + 12 \quad \text{(Subtract $4x$)} \\ y &= -2x + 6 \quad \ \text{(Divide by 2)} \end{align*}$$

• Slope: $-2$
• Y-intercept: $(0, 6)$

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2. Finding intercepts

• X-intercept ($y=0$): $4x + 2(0) = 12 \implies x = 3 \quad \rightarrow (3, 0)$

• Y-intercept ($x=0$):
  $4(0) + 2y = 12 \implies y = 6 \quad \rightarrow (0, 6)$

Graph the line through $(3, 0)$ and $(0, 6)$.

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Solution Set

All real solutions lie on the line $y = -2x + 6$. Example ordered pairs:

• When $x=1$: $y=4$ → $(1, 4)$
• When $x=2$: $y=2$ → $(2, 2)$
• When $x=-1$: $y=8$ → $(-1, 8)$

❓ Let me know if you'd like help with:

• Solving for specific values
• Converting to other forms
• Graphing techniques