the line perpendicular to 4y-2x=7/3 passing through (9, -2) write an equation for each line described express answer in point slope or slope intercept.
4 y = 2 x - 7/3
y = (1/2) x = 7/6
slope = 1/2
slope of perpendicular = -1/(1/2)
= -2
so we want
y = -2 x + b
plug point in to get b
-2 = -2(9) + b
b = 16
y = -2 x + 16
will you please explain it more
ok
I put the original line in the form
y = m x + b
then m, the slope was 1/2
m' the slope of a perpendicular = -1/m
so m' = -1/(1/2) = -2
so I know the line I am looking for is of form
y = -2 x + b
but I do not know b
so I put the x and y in for a point on that line and from that I can get b
You know that perpendicular lines have slopes that are negative reciprocals of each other.
Thus the new perpendicular line is
4x+2y= c
plug in your pont (9,-2)
36 - 4 = c = 32
4x + 2y = 32
2x + y = 16
To find the line perpendicular to the equation 4y-2x=7/3, we need to find the slope of that given line first.
Step 1: Convert the given equation into slope-intercept form (y = mx + b).
4y - 2x = 7/3
4y = 2x + 7/3
y = (2/4)x + 7/12
y = (1/2)x + 7/12
From the equation, we can see that the slope (m) of the given line is 1/2.
Step 2: Determine the slope of the line perpendicular to the given line.
The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line.
So, the slope of the perpendicular line would be -1/(1/2) = -2.
Step 3: Use the given point (9, -2) and the perpendicular slope (-2) to write the equation.
We will use the point-slope form of the equation: y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope.
Plugging in the values from the given point (9, -2) and the slope (-2), we get:
y - (-2) = -2(x - 9)
y + 2 = -2x + 18
To convert it into slope-intercept form, isolate y:
y = -2x + 16
Therefore, the equation of the line perpendicular to 4y-2x=7/3 and passing through (9, -2) is y = -2x + 16 in slope-intercept form.