Question: Rewrite the following equation in slope-intercept form. \[ 0 = 6x + 17y - 2 \] Write your…

Rewrite the following equation in slope-intercept form.

\[ 0 = 6x + 17y - 2 \]

Write your answer using integers, proper fractions, and improper fractions in simplest form.

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Solution

To rewrite the equation \(0 = 6x + 17y - 2\) in slope-intercept form, follow these steps: First, isolate \(y\) on one side of the equation. \[ 0 = 6x + 17y - 2 \] Add 2 to both sides: \[ 2 = 6x + 17y \] Subtract \(6x\) from both sides: \[ 2 - 6x = 17y \] Now, divide every term by 17: \[ y = \frac{-6}{17}x + \frac{2}{17} \] The slope-intercept form is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. Thus, the equation in slope-intercept form is: \[ y = \frac{-6}{17}x + \frac{2}{17} \]