Question

GEOMETRY!!!
Whats an equation of the line parallel to the given line that contains C?
C(6,0); y=1/3x

Answer 1

Given two lines:
\[y_1 = m_1x+b_1 \\ y_2 = m_2x+b_2\]

Do you know what makes those two lines parallel? (any two lines that is)

Answer 2

plug into y=mx+b and solve, then take what you got for b and take the current slope you have and make an equation

Answer 3

Nope, i have no clue. My teachers an idiot and wont teach crap.

Answer 4

Slope is usually denoted by the constant (m) in linear equations and is given by:
\[m \frac{y_2-y_1}{x_2-x_1} \]
Slope shows the change in y with respect to the change in x (if x changes 1 unit, how much will y change).

It refers to how steep a line is:

Two lines are parallel if their slopes are the same. So for example:

\[ y_1 = 2x+5\\
y_2 = 2x - 2 \]

These two lines are parallel because they both have a slope of 2, but different y intercepts. The general form of a line is given by:
\[ y = \underbrace{m}_{\text{slope}} x + \underbrace{b}_{\text{y-intercept}}\].

The b tells you where the line interesects the y axis.

Now for your problem. We know the slope of the first line is 1/3. So we know our new slope must be the same. We get the partial equation:
\[y = \frac{1}{3}x +b \]

We also know the line passes through (6,0). THis will help us solve for b. Plug in x=6 and y=0 into our equation and we get:
\[0 = \frac{1}{3}6 + b = 2+b \quad \to \quad b=-2\]

Solving for b gives us -2, we can then finally write our new line:
\[y = \frac{1}{3}x -2 \]