write equation of line that passes through the point
1)parallel to the given line
2)perpendicular to the given line
pt (6,2)
line -9x+9y=144
a)para -9x+9y=-72
perp -9x-9y=-36
b)para -9x-9y=-36
perp -9x-9y=-72
c)para 9x+9y=-36
perp 9x-9y=-72
d)para -9x-9y=-72
perp -9x-9y=-72
Write equations in the form
y = m x + b
then m is the slope
then put the coordinates in to get b
in this case
9 y = 9 x + 144
or
y = 1 x + 16
slope is 1 so parallel is
y = x + b
through (6,2)
2 = 6 + b
b = -4
so for parallel y = x - 4
or
9 y = 9 x - 36
9x - 9y = 36
So I get none of the above for the parallel line. Typo?
sorry I can't seem to type this morning
b) para -9x+9y=-36
perp -9x-9y=-72
ok for parallel
now perp
y = -x +b
(6,2)
2 = -6+b
b = 8
so
y = -1x + 8
9y = -9x + 72
-9x - 9y = -72 yes
To find the equation of a line that is parallel or perpendicular to a given line and passes through a specific point, you need to consider the slope of the given line.
1) To find the equation of a line parallel to the given line:
- The parallel line will have the same slope as the given line.
- Start by rearranging the given line equation into the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
- Calculate the slope of the given line by dividing the coefficient of x by the coefficient of y.
- Once you have the slope, substitute the slope and the coordinates of the point (6,2) into the slope-intercept form to find the value of b.
- Write the equation using the slope-intercept form.
2) To find the equation of a line perpendicular to the given line:
- The perpendicular line will have a negative reciprocal slope compared to the given line.
- Start by finding the slope of the given line using the same method as in step 1.
- Calculate the negative reciprocal of the slope.
- Substitute the negative reciprocal slope and the coordinates of the point (6,2) into the slope-intercept form to find the value of b.
- Write the equation using the slope-intercept form.
Now let's evaluate each option given and determine the correct answer:
a) para -9x+9y=-72
perp -9x-9y=-36
- The coefficient of x is the same in both lines, but the coefficient of y differs, so option a) is incorrect.
b) para -9x-9y=-36
perp -9x-9y=-72
- The coefficients of both x and y are the same in both lines, so option b) is incorrect.
c) para 9x+9y=-36
perp 9x-9y=-72
- The coefficients of both x and y are positive in the parallel line equation, which is incorrect. However, the coefficients of x and y are correct for the perpendicular line equation.
d) para -9x-9y=-72
perp -9x-9y=-72
- The coefficients of both x and y are the same in both lines, so option d) is incorrect.
Therefore, the correct answer is option c), which represents the equation of a line perpendicular to the given line and passes through the point (6,2):
-9x + 9y = -72