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=-\frac{4}{2}-\frac{1}{2}x=-2+\frac{1}{2}x$

So, if we organice that:

$y=\frac{1}{2}x-2$

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=\frac{1}{2}(2)+b$$2=1+b\Rightarrow2-1=b$$1=b$Knowing that, the equation is:$y=\frac{1}{2}x+1$