Questions: Find the equation of the line with slope -3 which goes through the point (6,-7). Give your answer in slope-intercept form y=mx+b.

Find the equation of the line with slope -3 which goes through the point (6,-7). Give your answer in slope-intercept form y=mx+b.
Transcript text: Find the equation of the line with slope -3 which goes through the point $(6,-7)$. Give your answer in slope-intercept form $y=m x+b$. Provide your answer below: \[ y=\square \]
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Solution

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Solution Steps

Step 1: Start with the general equation of a line in slope-intercept form

The general form is \(y = mx + b\).

Step 2: Substitute the given slope (\(m\)) into the equation

Substituting the given slope, the equation becomes \(y = -3x + b\).

Step 3: Use the given point to find \(b\)

Substituting the point \((6, -7)\) into the equation, we get \(-7 = -3(6) + b\). Solving for \(b\), we find \(b = -7 + 3(6) = 11\).

Final Answer:

The equation of the line is \(y = -3x + 11\).

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