Question

Write an equation in​ slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation.
​(0,0); y equals one eighth x plus 2
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Part 1
The equation of the line is yequals
  
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Answer 1

To write the equation of a line in slope-intercept form (y = mx + b) that is parallel to a given line, we need to:

1. Identify the slope of the given line.
2. Use the slope and the point provided to find the equation of the new line.

The given equation is:

\[ y = \frac{1}{8}x + 2 \]

Here, the slope (m) is \(\frac{1}{8}\).

Since parallel lines have the same slope, the slope of the new line will also be \(\frac{1}{8}\).

Now, we will use the point (0, 0) to find the y-intercept (b) of the new line. We can substitute the coordinates of the point into the slope-intercept equation:

Let:
- x = 0
- y = 0

Substituting these into the slope-intercept form \(y = mx + b\):

\[
0 = \frac{1}{8}(0) + b
\]

This simplifies to:

\[
0 = b
\]

Thus, the y-intercept (b) is 0.

Now we can write the equation of the line:

\[
y = \frac{1}{8}x + 0
\]

or simply:

\[
y = \frac{1}{8}x
\]

So the final equation of the line is:

**y = \(\frac{1}{8}x\)**.