Questions: Consider the line y=-5x+9. Find the equation of the line that is perpendicular to this line and passes through the point (8,-3). Find the equation of the line that is parallel to this line and passes through the point (8,-3). Note that the ALEKS graphing calculator may be helpful in checking your answer. Equation of perpendicular line: Equation of parallel line:

Solution Steps

The slope of the parallel line is equal to the slope of the given line, which is \(m = -5\).

Using the point-slope form equation, we substitute \(m = -5\) and the point \((8, -3)\), to get the equation of the parallel line in slope-intercept form: \(y = -5x + 37\).

The slope of the perpendicular line is the negative reciprocal of the slope of the given line, which is \(m_{perpendicular} = -\frac{1}{-5} = 0.2\).

Using the point-slope form equation, we substitute \(m = 0.2\) and the point \((8, -3)\), to get the equation of the perpendicular line in slope-intercept form: \(y = 0.2x - 4.6\).

Final Answer: