To find the equation of a line parallel to the line x + 2y = -2, we need to keep the slope of the new line the same as the slope of the given line. The given line can be rewritten in slope-intercept form as y = -0.5x - 1.
Since the slope of the given line is -0.5, the slope of the line parallel to it will also be -0.5.
Using the point-slope form of the equation for a line, we have:
y - y1 = m(x - x1)
y - 4 = -0.5(x + 5)
y - 4 = -0.5x - 2.5
y = -0.5x + 1.5
So, the equation of the line parallel to x + 2y = -2 and passing through the point (-5, 4) is y = -0.5x + 1.5.
To find the equation of a line perpendicular to x + 2y = -2, we need to find the negative reciprocal of the slope of the given line, which is 2.
Using the point-slope form of the equation for a line, we have:
y - y1 = m(x - x1)
y - 4 = 2(x + 5)
y - 4 = 2x + 10
y = 2x + 14
So, the equation of the line perpendicular to x + 2y = -2 and passing through the point (-5, 4) is y = 2x + 14.
Consider the line x + 2y = -2.
Find the equation of the line that is parallel to this line and passes through the point (-5, 4).
Find the equation of the line that is perpendicular to this line and passes through the point (-5, 4).
Note that the ALEKS graphing calculator may be helpful in checking your answer.
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