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)
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.`