Question 761679
Given line y = x + 8.

Principle 1: Any line expressed in the form {{{y = m*x + c}}} has slope = m.

It has the y intercept (the point where it intersects the y axis as c.

(The more general form of a linear equation is ax + by = c, which can also be converted to the y = mx + c form.)

Principle 2: Lines parallel to each other have the same slope

Here the given line is already in the form y = mx + c

y = x + 8.

Slope of the given line = 1.

The parallel line also has slope 1 and passes through (2,16).

How can we express the second line also  as y = mx + c?

m is the slope and c is the y intercept

We know m (which is 1), and we know one instance of x,y i.e. (2,16). We do not know the y intercept c.

Substituting for one value of x, y and m, we can find c.

{{{16 = 2*1 + c}}} or {{{c = 14}}}.

So, the equation to the second line is {{{y = x + 14}}}

:)