10. Write an equation of a line that passes through the point $(9,-3)$ and is parallel to the following equation: $9 x+7 y=330$
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Answer
Final Answer: The equation of the line that passes through the point \((9,-3)\) and is parallel to the line \(9x + 7y = 330\) is \(\boxed{y = -1.29x + 8.57}\).
Step 1 ：The equation of a line in the slope-intercept form is given by \(y = mx + c\), where \(m\) is the slope and \(c\) is the y-intercept.
Step 2 ：The slope of a line given by the equation \(ax + by = c\) is \(-a/b\).
Step 3 ：Since parallel lines have the same slope, the slope of the line we are looking for is the same as the slope of the given line.
Step 4 ：We can find the y-intercept by substituting the coordinates of the given point into the equation of the line and solving for \(c\).
Step 5 ：Given that \(a = 9\), \(b = 7\), \(x = 9\), and \(y = -3\), we can calculate \(m = -1.29\) and \(c = 8.57\).
Step 6 ：Final Answer: The equation of the line that passes through the point \((9,-3)\) and is parallel to the line \(9x + 7y = 330\) is \(\boxed{y = -1.29x + 8.57}\).
