To convert the standard form equation [tex]\( 6x - 2y = -20 \)[/tex] into slope-intercept form, follow these steps:
1. Start with the given equation:
[tex]\[ 6x - 2y = -20 \][/tex]
2. Isolate the term involving [tex]\(y\)[/tex] on one side of the equation. To do this, move the [tex]\(6x\)[/tex] term to the right side by subtracting [tex]\(6x\)[/tex] from both sides:
[tex]\[ -2y = -6x - 20 \][/tex]
3. Solve for [tex]\(y\)[/tex] by dividing every term by [tex]\(-2\)[/tex]:
[tex]\[ y = \frac{-6x}{-2} + \frac{-20}{-2} \][/tex]
4. Simplify the fractions:
[tex]\[ y = 3x + 10 \][/tex]
Therefore, the slope-intercept form of the equation is:
[tex]\[ y = 3x + 10 \][/tex]
