write an equation of the line containing the point and perpendicular to the given line (4,-8); 2x+5y=4
I am having a very hard time, but I'm trying hard to study the steps for solving the problem.
Profoundly, thank you.
Did you see the answer to your post below?
Post your work so I can see where you are having trouble.
Sorry, but, no, I didn't see the answer to my post. However,
(4,-8); 2x+5y=4 is?
y=-2x+4
y-8=1/2
y-8=1/2(x-4)
Again, I don't really know what to do after this. I may not even be followin the steps right. However, I would really appreacite your help. Thank you a million.
2x + 5y = 4
Add -2x to both sides
5y = -2x + 4
divide both sides by 5
y = -2/5 y + 4/5
So, slope m = -2/5
Perpendicular lines, the slopes are negative reciprocals of each other.
Slope = -2/5
m1 * m2 = -1
-2/5 * m2 = -1
m2 = -1/(-2/5)
m2 = 5/2
Now you have to find b, for the equation of the perpendicular line.
y = mx + b
m = 5/2
y = 5/2 x + b
P(4, -8)
-8 = 5/2 (4) + b
-8 = 20/2 + b
-8 = 10 + b
-18 = b
y = 5/2 x + b
y = 5/2 + -18
y = 5/2 - 18
Follow these exact steps.
To find the equation of a line perpendicular to the given line, you need to follow these steps:
Step 1: Determine the slope of the given line.
Step 2: Find the negative reciprocal of the slope from Step 1. This will be the slope of the perpendicular line.
Step 3: Use the point (4,-8) along with the slope from Step 2 to find the equation of the line.
Let's go through each step in detail:
Step 1: Determine the slope of the given line.
The given line has the equation 2x + 5y = 4. To find the slope, you need to put this equation in slope-intercept form (y = mx + b), where m represents the slope.
Rearrange the given equation in slope-intercept form:
2x + 5y = 4
5y = -2x + 4
y = (-2/5)x + 4/5
The slope of the given line is -2/5.
Step 2: Find the negative reciprocal of the slope from Step 1.
The negative reciprocal of -2/5 is 5/2. So, the slope of the perpendicular line is 5/2.
Step 3: Use the point (4,-8) and the slope from Step 2 to find the equation of the line.
Now that you have the slope (m = 5/2) and a point (4,-8), you can use the point-slope form of a line to find the equation.
The point-slope form of a line is: y - y1 = m(x - x1)
Using the given point (4,-8) and the slope 5/2, substitute the values into the point-slope form:
y - (-8) = (5/2)(x - 4)
y + 8 = (5/2)(x - 4)
Simplify if needed:
y + 8 = (5/2)x - 10
y = (5/2)x - 18
Therefore, the equation of the line containing the point (4,-8) and perpendicular to the line 2x + 5y = 4 is y = (5/2)x - 18.