Which Is equation in slope intercept form for the line passes through (2,8) and is perpendicular to 4x+2y=6
y=-1/2x+7
y=1/2x+7
y=-2x+12
y=2x+4
Love you and thanks for the help
sticking with the standard form, if
4x+2y=6 is a line, then a perpendicular line would be
2x - 4y = c
plug in your given point (2,8)
4 - 32 = c
c = -28
new equation:
2x - 4y = -28
x - 2y = -14
now switch to other form
-2y = -x - 14
divide both sides by -2
y = (-1/2)x + 7 , I see that
4x+2y = 6.
m = -A/B = -4/2 = -2.
(2, 8).
Y = mx+b
m = -(-1/2) = 1/2.
8 = (1/2)2 + b,
b = 7.
Eq: Y = (1/2)x + 7.
To find the equation of a line that is perpendicular to a given line, we first need to determine the slope of the given line.
The given line, 4x + 2y = 6, is not yet in slope-intercept form (y = mx + b), so we should rearrange it to solve for y:
2y = -4x + 6 (subtracting 4x from both sides)
y = -2x + 3 (dividing both sides by 2)
The slope of the given line is -2, because it is the coefficient of x.
Now, to find the slope of a line perpendicular to the given line, we take the negative reciprocal of the slope. The negative reciprocal of -2 is 1/2.
So the equation of the line passing through the point (2,8) and perpendicular to 4x + 2y = 6 will have a slope of 1/2. We can now use the point-slope form of the equation:
y - y1 = m(x - x1)
Substituting the values (2,8) and m = 1/2:
y - 8 = 1/2(x - 2)
Simplifying:
y - 8 = 1/2x - 1 (distributing 1/2 to x and -2)
y = 1/2x + 7 (adding 8 to both sides)
Therefore, the equation in slope-intercept form for the line that passes through (2,8) and is perpendicular to 4x + 2y = 6 is y = 1/2x + 7.