Consider the line y=-8/9x-2
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.
To find the equation of the line that is perpendicular to y = -8/9x - 2, we first need to find the slope of the given line. The slope of the given line is -8/9.
The slope of a line perpendicular to this line will be the negative reciprocal of -8/9, which is 9/8.
Now, we can use the point-slope form of the equation of a line to find the equation of the perpendicular line passing through (8, -3):
y - y1 = m(x - x1)
y - (-3) = 9/8(x - 8)
y + 3 = 9/8x - 9
y = 9/8x - 12
Therefore, the equation of the line perpendicular to y = -8/9x - 2 and passing through (8, -3) is y = 9/8x - 12.
To find the equation of the line parallel to y = -8/9x - 2, we know that parallel lines have the same slope.
Therefore, the equation of the line parallel to y = -8/9x - 2 and passing through (8, -3) will also have a slope of -8/9.
Using the point-slope form of the equation of a line:
y - y1 = m(x - x1)
y - (-3) = -8/9(x - 8)
y + 3 = -8/9x + 64/9
y = -8/9x + 64/9 - 27/9
y = -8/9x + 37/9
Therefore, the equation of the line parallel to y = -8/9x - 2 and passing through (8, -3) is y = -8/9x + 37/9.