Write an equation of the the line containing the given point and perpendicular to the given line. (7,-5); 9x+7y = 3.
What I have so far. y-9=(1/9(x-3). Not sure after this.
First of all the new slope should have been 7/9.
Now you have to use the given point this way ...
y + 5 = (7/9)(x-7)
multiply each side by 9 (I don't like fractions in my equations)
9y + 45 = 7x - 49
-7x + 9y = -93
7x - 9y = 93
A quick way to do the above..
If Ax + By = C is the equation , then
the line Bx - Ay = K is perpendicular to it,
so
if 9x + 7y = 3 is given , then
7x - 9y = k is the perpendicular line
sub in the given point ...
7(7) - 9(-9) = c = 93
7x - 9y = 93 is your new line
thank u
To find the equation of a line perpendicular to another line, we need to start by finding the slope of the given line.
Given line: 9x + 7y = 3
We can rewrite this equation in slope-intercept form (y = mx + b) by isolating y:
7y = -9x + 3
y = (-9/7)x + 3/7
The slope of the given line is -9/7.
The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line. Therefore, the slope of the line we want to find is 7/9.
Now, we can use the point-slope form to find the equation of the line. We have a point (7, -5) and a slope of 7/9.
The point-slope form is given by: y - y1 = m(x - x1)
Substituting the values, we get:
y - (-5) = (7/9)(x - 7)
y + 5 = (7/9)(x - 7)
To simplify further, we can distribute the (7/9) to the terms inside the parentheses:
y + 5 = (7/9)x - (49/9)
Finally, we can rearrange the equation to get it in standard form:
(7/9)x - y = (49/9) - 5
(7/9)x - y = (49/9) - (45/9)
(7/9)x - y = 4/9
Therefore, the equation of the line perpendicular to 9x + 7y = 3 and passing through the point (7, -5) is (7/9)x - y = 4/9.
To find the equation of a line perpendicular to a given line, we need to determine the slope of the given line and then find the negative reciprocal of that slope. Once we have the slope of the perpendicular line, we can find the equation using the given point.
First, let's rearrange the given line equation into slope-intercept form (y = mx + b) by isolating y:
9x + 7y = 3
7y = -9x + 3
y = (-9/7)x + 3/7
From this equation, we can see that the slope of the given line is -9/7. To find the slope of the perpendicular line, we take the negative reciprocal of -9/7, which gives us 7/9.
Now, we have the slope of the perpendicular line, which is 7/9, and also the given point (7, -5).
We can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Plugging in the values, we get:
y - (-5) = (7/9)(x - 7)
y + 5 = (7/9)(x - 7)
Expanding and simplifying the equation further:
y + 5 = (7/9)x - 49/9
y = (7/9)x - 49/9 - 45/9
y = (7/9)x - 94/9
Therefore, the equation of the line containing the point (7, -5) and perpendicular to the line 9x + 7y = 3 is y = (7/9)x - 94/9.