Question

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1. -6x + 3y = -9
2. 5x - y = 1
3. 2y - 3x = 10
4. 2y + x = 14
5. x - 4y - 8 = 0
6. 3y + 18 = -8x + 3 (with some work shown: subtracting 18, dividing by 3 to get y = -8/3 x - 5)
7. 9x - 2y = 7
8. x + 5y = 8x - 20
9. -2(3y - 1) - x = 0 (with some work shown, ending with y = -1/6 x + 1/3)
10. 2x - y = -1
11. 3y + 2x + 12 = 0
12. 4y + 20 = 5x
13. 3(x - 1) = 2x - y (with work shown, ending with y = -x + 3)
14. 7x - 1 = 3y + 8
15. 9x + 18y = 0

Explanation:

Let's solve equation 1: \(-6x + 3y = -9\) for \(y\) in slope - intercept form (\(y=mx + b\)).

Step 1: Isolate the term with \(y\)

Add \(6x\) to both sides of the equation.
\(-6x+3y + 6x=-9 + 6x\)
Simplifying, we get \(3y=6x - 9\)

Step 2: Solve for \(y\)

Divide each term in the equation \(3y = 6x-9\) by 3.
\(y=\frac{6x}{3}-\frac{9}{3}\)
Simplifying the fractions, we have \(y = 2x-3\)

Answer:

For the equation \(-6x + 3y=-9\), the slope - intercept form is \(y = 2x-3\)