Write an equation of the line containing the given point and perpendicular to the given line. express your answer in the form y=mx+b.
(-5,7); 2x=9y+4
the equation of the line is y=?
I answered the same type of question for you in
http://www.jiskha.com/display.cgi?id=1253635946
follow those steps
To find the equation of the line perpendicular to the given line, we need to determine the slope of the given line and then find the negative reciprocal of that slope.
First, let's rewrite the given equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
2x = 9y + 4
Subtract 9y and 4 from both sides:
2x - 4 = 9y
Now divide both sides by 9:
(2/9)x - (4/9) = y
The slope (m) of the given line is 2/9.
For the line perpendicular to this line, the slope will be the negative reciprocal of 2/9. To find the negative reciprocal, flip the fraction and change its sign:
Negative reciprocal of 2/9 = -9/2
So the slope of the perpendicular line is -9/2.
Now let's use the point-slope form (y - y1 = m(x - x1)) to find the equation of the line. We'll substitute the values of the point (-5, 7) and the slope (-9/2) into the equation:
y - 7 = (-9/2)(x - (-5))
Simplify:
y - 7 = (-9/2)(x + 5)
Distribute (-9/2) across (x + 5):
y - 7 = (-9/2)x - (45/2)
Combine like terms:
y = (-9/2)x - (45/2) + 7
simplifying further:
y = (-9/2)x - 45/2 + 14/2
y = (-9/2)x - 31/2
Therefore, the equation of the line perpendicular to 2x = 9y + 4, and passing through the point (-5,7), is y = (-9/2)x - 31/2.
To find the equation of the line containing the given point (-5,7) and perpendicular to the line 2x=9y+4, we first need to determine the slope of the given line.
Rewriting the given equation in the standard form y=mx+b, we have:
2x=9y+4
Dividing both sides by 9, we get:
(2/9)x = y + 4/9
Now, let's compare this equation to standard form y=mx+b. We can see that the slope (m) of the given line is 2/9.
To find the slope of a line perpendicular to this given line, we use the fact that perpendicular lines have slopes that are negative reciprocals of each other. So the slope of the perpendicular line will be the negative reciprocal of 2/9.
The negative reciprocal of 2/9 can be found by flipping the fraction and changing the sign, so the slope of the perpendicular line is -9/2.
Now that we have the slope (-9/2), we can use the point-slope form of a line to find the equation of the perpendicular line. The point-slope form is given by y - y1 = m (x - x1), where (x1, y1) are the coordinates of the given point.
Using the coordinates (-5,7) and the slope -9/2, we have:
y - 7 = (-9/2)(x - (-5))
Simplifying this equation further:
y - 7 = (-9/2)(x + 5)
Distributing the -9/2:
y - 7 = (-9/2)x - (9/2)(5)
y - 7 = (-9/2)x - 45/2
Adding 7 to both sides:
y = (-9/2)x - 45/2 + 7
y = (-9/2)x - 45/2 + 14/2
y = (-9/2)x - 31/2
Therefore, the equation of the line perpendicular to 2x=9y+4 and passing through the point (-5,7) is y = (-9/2)x - 31/2 in slope-intercept form.