Question

Find the equation of the line passing through point (2,5) and parallel to y = -1/2x -2

Answer 1

We are told to find the equation of the line passing through the points (2, 5) and parallel to

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

Now, equation of line in slope intercept form is given as

`y=mx+b`

comparing this to

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

We can see that m for that equation is

`-(1)/(2)`

m is the slope.

For two parallel lines, m1 = m2. That is their slopes are equal.

So we will use our m as

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

For equation of line for point and slope form, we have the formula as

`y-y_1=m(x-x_1)`

using this, the equation of the line becomes

`\begin{gathered} y-y_1=m(x-x_1) \\ \\ y-5_{}=-(1)/(2)(x-2) \\ \\ y-5=-(x)/(2)+(2)/(2) \\ \\ y-5=-(x)/(2)+1 \\ \\ y=-(x)/(2)+6 \\ \\ y=-(1)/(2)x+6 \end{gathered}`

Therefore, option C is the correct answer