Question

FInd the equation of the line that passes through (1,3) and is perpendicular to y=1-2x. Leave your answer in the form ax+by=c Where a,b and c are integers.​

Answer 1

`y = \frac{x}2 + 2.5`

Explanation:

Step 1) Finding the slope
The line is perpendicular to
`y = 1 - 2x`, therefore, its slope is equal to the negative invert of
`y`'s slope.

`y`'s slope is -2 (the coefficient to
`x`), and, therefore, the line's slope is
`m = [-(-2)]^(-1) = 2^(-1) = \frac12`

Step 2) Building the Equation

We can now substitute the slope, along with the given point's coordinates, into the formula
`y - y_1 = m(x - x_1)` :

`y - 3 = \frac12(x - 1)\\\to y - 3 = \frac{x}2 - \frac12\\\to y = \frac{x}2 + 2.5`