Question

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write -5x + 15y = -30 in slope - intercept form. \\( y = \frac{1}{3}x + 2 \\) \\( y = \frac{1}{3}x - 2 \\) \\( y = -\frac{1}{3}x + 2 \\) \\( y = -\frac{1}{3}x - 2 \\)

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a linear equation is \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. We need to solve the given equation \(- 5x+15y=-30\) for \(y\).

Step2: Isolate the term with \(y\)

Add \(5x\) to both sides of the equation \(-5x + 15y=-30\).
We get \(15y=5x - 30\). The reason for this step is to get the \(y\) - term alone on one side of the equation. The equation after adding \(5x\) to both sides is derived from the addition property of equality, which states that if \(a = b\), then \(a + c=b + c\). Here, \(a=-5x + 15y\), \(b = - 30\) and \(c = 5x\).

Step3: Solve for \(y\)

Divide each term in the equation \(15y=5x - 30\) by \(15\).
For the first term: \(\frac{15y}{15}=\frac{5x}{15}-\frac{30}{15}\)
Simplify each term: \(y=\frac{1}{3}x-2\)

Answer:

\(y = \frac{1}{3}x-2\) (corresponding to the option \(y=\frac{1}{3}x - 2\))