Question

What is an equation of the line that passes through the point (2, 2) and is parallel tothe line x - 2y = 42

Answer 1

When two lines are parallel it means that they have the same slope:

First we need to know that the general formula for a lineal equation is:

`y=mx+b`

So, we have the ecuation x - 2y = 42 we can put it in the general way by clearing the y as follow:

`x-2y=4`
`-2y=4-x\text{ }`
`y=-(4)/(2)-(1)/(2)x=-2+(1)/(2)x`

So, if we organice that:

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

So the scope in this equation is: m=1/2. It means that the equation parallel to it have also slope m=1/2

Now, we can use the point (2,2) to find the value of the b in the lineal equation formula, as follow:

x=2

y=2

`y=mx+b\text{ }\Rightarrow2=(1)/(2)(2)+b`
`2=1+b\Rightarrow2-1=b`
`1=b`Knowing that, the equation is:
`y=(1)/(2)x+1`