Question

consider the line 9x + 7y = -3. what is the slope of a line parallel to this line? what is the slope of a line perpendicular to this line? slope of a parallel line: slope of a perpendicular line:

Explanation:

Step1: Convert to slope - intercept form

The equation of a line in slope - intercept form is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.
We start with the equation \(9x+7y=-3\).
Subtract \(9x\) from both sides: \(7y=-9x - 3\).
Divide each term by \(7\): \(y=-\frac{9}{7}x-\frac{3}{7}\).
So the slope of the given line \(m = -\frac{9}{7}\).

Step2: Find slope of parallel line

Parallel lines have the same slope. So the slope of a line parallel to the line \(9x + 7y=-3\) is equal to the slope of the given line.
Since the slope of the given line is \(-\frac{9}{7}\), the slope of the parallel line is \(-\frac{9}{7}\).

Step3: Find slope of perpendicular line

The slope of a line perpendicular to a line with slope \(m\) is the negative reciprocal of \(m\).
If \(m = -\frac{9}{7}\), the negative reciprocal \(m_{\perp}=-\frac{1}{m}\) (when \(m
eq0\)).
So \(m_{\perp}=-\frac{1}{-\frac{9}{7}}=\frac{7}{9}\).

Answer:

Slope of a parallel line: \(-\frac{9}{7}\)
Slope of a perpendicular line: \(\frac{7}{9}\)