Question

Find the equation of the line that passes through (-1,3) and is perpendicular to 2y=x−1. Leave your answer in the form y=mx +c Another one of these and i still don't get it :(

Answer 1

y = -2x + 1.

Explanation:

2y = x - 1

y = 1/2y - 1/2

If line X is perpendicular to line Y (the line where y = 1/2y - 1/2), the slope will be the negative reciprocal of line Y. That means that there will be a negative sign instead of positive, and the 1/2 will be flipped to become 2/1, which is 2.

So, the slope will be -2.

We now have y = -2x + c.

To find c, simply put in -1 for x and 3 for y.

3 = -2 * -1 + c

c + 2 * 1 = 3

c + 2 = 3

c = 1

So, the equation of the line is y = -2x + 1.

Hope this helps!

Answer 2

Answer: y = -2x + 1

Explanation:

Perpendicular means they have opposite reciprocal slopes.

Rewrite 2y = x - 1 in Slope-Intercept format by dividing everything by 2:

`y=(1)/(2)x-(1)/(2)\\\\slope(m) = (1)/(2)\qquad \rightarrow \qquad m_\perp = -2`

Next, Use the Point-Slope formula where (x₁, y₁) = (-1, 3) and m = -2

y - y₁ = m (x - x₁)

`y-(3)=-2\bigg(x-(-1)\bigg)\\\\\\y-3=-2x-2\\\\\\y=-2x-2+3\\\\\\\large\boxed{y=-2x+1}\\`