The equation of a straight line l1 is 3y+4x=12.Find the equation of another line l2 which is perpendicular to l1 and passes through [1, -2].
First we need to find the slope of the line l1. We can rearrange the equation to solve for y:
3y + 4x = 12
3y = -4x + 12
y = (-4/3)x + 4
The slope of l1 is therefore -4/3.
To find the slope of the line l2, we know that it must be the negative reciprocal of the slope of l1.
Slope of l2 = 3/4
Now we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Where m is the slope and (x1, y1) is a point on the line.
We know that (x1, y1) = (1, -2) and m = 3/4, so:
y - (-2) = (3/4)(x - 1)
y + 2 = (3/4)x - 3/4
y = (3/4)x - 11/4
So the equation of line l2 is y = (3/4)x - 11/4.
Just a note:
Since the first line was expressed in standard form, maybe the second should also be in standard form:
3x-4y = 11
Yes, you are correct. Thank you for bringing this to my attention.
To convert the equation of line l2 to standard form, we can rearrange it as follows:
y = (3/4)x - 11/4
-3/4 x + y = -11/4
Multiplying both sides by -4 to eliminate the fraction:
3x - 4y = 11
So the equation of line l2 in standard form is 3x - 4y = 11, which is perpendicular to line l1 and passes through the point (1, -2).
To find the equation of a line perpendicular to line l1, we can use the fact that the slopes of perpendicular lines are negative reciprocals of each other.
First, let's rearrange the equation of line l1 to the form y = mx + b, where m is the slope and b is the y-intercept.
The equation of line l1 is 3y + 4x = 12. Let's rearrange this equation to solve for y:
3y = -4x + 12
y = (-4/3)x + 4
So, the slope of line l1 is -4/3.
To find the slope of line l2, which is perpendicular to l1, we can take the negative reciprocal of -4/3.
The negative reciprocal of -4/3 is 3/4.
Now, we have the slope (m = 3/4) and a point on line l2 (1, -2).
We can use the point-slope form of the equation of a line to find the equation of line l2:
y - y1 = m(x - x1)
Substituting the given values, we have:
y - (-2) = (3/4)(x - 1)
y + 2 = (3/4)x - 3/4
y = (3/4)x - 3/4 - 2
y = (3/4)x - 3/4 - 8/4
y = (3/4)x - 11/4
Therefore, the equation of line l2, which is perpendicular to line l1 and passes through the point (1, -2), is y = (3/4)x - 11/4.