Find the equation of the line perpendicular to line 2x−5y−10=0 and containing point (−1, 5).
Easy way to do these:
Since the lines are perpendicular, their slopes must be negative reciprocals of each other.
So just interchange the x and y coefficients, and change the sign on one of them,
then sub in the given point to find the constant.
2x−5y−10=0 ---> 5x + 2y = C
using (−1, 5) ---> 5(-1) + 2(5) = C
C = 5
new equation: 5x + 2y = 5
Oh my! Which gives the exact same answer Layla replied with!
I had a negative sign incorrect!
Great job team!
I'm sorry Ms. Pi, but you didn't do anything. You aren't part of the team.
To find the equation of a line perpendicular to another line, you need to determine the slope of the given line and then find the negative reciprocal of that slope.
Let's start with the given equation of the line: 2x - 5y - 10 = 0.
To find the slope of this line, we need to rearrange the equation into slope-intercept form (y = mx + b) where "m" represents the slope.
So, let's rewrite the given equation:
2x - 5y - 10 = 0
-5y = -2x + 10
y = (2/5)x - 2
From this equation, we can see that the slope of the given line is 2/5.
Now, to find the slope of the line perpendicular to this, we take the negative reciprocal of 2/5.
The negative reciprocal of 2/5 is -5/2.
So, the slope of the perpendicular line is -5/2.
Now that we have the slope of the perpendicular line and a point it goes through (-1, 5), we can use the point-slope form of a line to find its equation.
The point-slope form is given as:
y - y1 = m(x - x1)
Where (x1, y1) represents the coordinates of the given point and m is the slope.
Substituting the values into the formula, we get:
y - 5 = (-5/2)(x - (-1))
Simplifying further:
y - 5 = (-5/2)(x + 1)
Expanding the equation:
y - 5 = (-5/2)x - 5/2
Now, rearrange the equation to isolate y:
y = (-5/2)x - 5/2 + 5
Simplifying further:
y = (-5/2)x + 5/2 - 10/2
y = (-5/2)x - 5/2
Therefore, the equation of the line perpendicular to 2x - 5y - 10 = 0 and containing the point (-1, 5) is y = (-5/2)x - 5/2.
Slope of original line: 2/5
Slope of perpendicular line: -5/2 [negative reciprocal]
Slope of new line should be: y=-5/2x + 5/2
Re-arrange the equation in y=mx + b
then look at the slope (m)
then use the perpendicular slope (-5/2), and the point (-1, 5) and solve for b : )
Lyla is incorrect... she did not sub in her point and solve for b : (
BUT here perpendicular slope is correct : ) a good starting point : )