# Find the appropriate equations and points from the questions below.  Simplify your equations into slope-intercept form.  Write the equation of a line parallel to the given line but passing through...

Find the appropriate equations and points from the questions below.

Simplify your equations into slope-intercept form.

Write the equation of a line parallel to the given line but passing through the given point.

Y= 3/4 x -1 ; ( 4,0)

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Since the problem provides the equation of a line, parallel to the line whose equation you need to find, and a point `(4,0), ` you may write the point slope form of equation of parallel line such that:

`y - 0 = m_2(x - 4)`

You may find the slope `m_1`  using the relation between the slopes of two parallel lines such that:

`m_1 = m_2`

You may use the given equation of the line `y = 3/4 x - 1` , to find the slope `m_2`  such that:

Notice that m_1 is the leading coefficient, hence, `m_1 = 3/4` , thus `m_2 = 3/4` .

Substituting `3/4`  for `m_2`  in equation of parallel line yields:

`y = (3/4)(x - 4) => y = 3/4 x - 3`

Hence, evaluating the slope intercept form of equation of the parallel line to the given line `y = 3/4 x - 1`  yields `y = 3/4 x - 3.`

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