Question

(4,-1); y=2x-4 write an equation through the point and perpendicular to the given line

Answer 1

y = (-1/2)x + 1

Explanation:

perpendicular?

flip the slope and make it negative

m = 2x -> (-1/2)x

line formula

y - y1 = m (x - x1)

(4,-1)

x1 = 4

y1 = -1

m = (-1/2)x

y - y1 = m (x - x1)

y - (-1) = (-1/2)(x - 4)

y + 1 = (-1/2)x + 2

y = (-1/2)x + 1.

bard & claude AI

Answer 2

`y =(-1)/(2)x + 1`

Explanation:

Product of slope of perpendicular lines = -1.

First find the slope of the equation, y = 2x - 4.

Slope y-intercept from of the equation: y = mx + b

Here, m is the slope.

m = 2

`\text{\bf Slope of the line perpendicular to y = 2x- 4 = } \ m_1 = (-1)/(m)`

`m_1 =(-1)/(2)`

Equation of the required line:

`\sf y = (-1)/(2)x + b`

Now, this line is passing through the point (4,-1). Substitute the co-ordinates in the above equation and find the value of y-intercept, b.

`\sf -1 = (-1)/(2)*4+b\\\\\\-1 = -2 + b\\\\`

-1 + 2 = b

`\boxed{\bf b = 1}`

Equation of the line:

`\boxed{\bf y =(-1)/(2)x + 1}`