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:

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:
Transcript text: Consider the line $y=-5 x+9$. 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: $\square$ Equation of parallel line:
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Solution

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Solution Steps

Step 1: Find the Slope of the Parallel Line

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

Step 2: Find the Equation of the Parallel Line

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: \(y = -5x + 37\).

Step 3: Find the Slope of the Perpendicular Line

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

Step 4: Find the Equation of the Perpendicular Line

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:

The equation of the line parallel to the given line and passing through the point \((8, -3)\) is \(y = -5x + 37\). The equation of the line perpendicular to the given line and passing through the point \((8, -3)\) is \(y = 0.2x - 4.6\).

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