To find the equation of the line that is perpendicular to y = -5/2x - 5, we first need to find the slope of the given line. In the standard form of a linear equation y = mx + b, m represents the slope of the line. In the equation y = -5/2x - 5, the slope is -5/2.
The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line. So the slope of the line perpendicular to y = -5/2x - 5 is 2/5.
Now we use the point-slope form of a linear equation (y - y1 = m(x - x1)) to find the equation of the line passing through the point (-2, 4) with slope 2/5:
y - 4 = 2/5(x + 2)
y - 4 = 2/5x + 4/5
y = 2/5x + 24/5
Therefore, the equation of the line that is perpendicular to y = -5/2x - 5 and passes through the point (-2, 4) is y = 2/5x + 24/5.
To find the equation of the line that is parallel to y = -5/2x - 5, we use the fact that parallel lines have the same slope. So the slope of the parallel line is also -5/2.
Using the point-slope form and the point (-2, 4), we get:
y - 4 = -5/2(x + 2)
y - 4 = -5/2x - 5
y = -5/2x - 1
Therefore, the equation of the line that is parallel to y = -5/2x - 5 and passes through the point (-2, 4) is y = -5/2x - 1.
Consider the line y = -5/2x -5
Find the equation of the line that is perpendicular to this line and passes through the point (-2, 4).
Find the equation of the line that is parallel to this line and passes through the point (-2, 4).
Note that the ALEKS graphing calculator may be helpful in checking your answer.
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