Examine if the lines are perpendicular?

D1 x+4y=11

D2 4x=y+21

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You need to verify if the slopes of the given lines check the equation that relates the slopes of perpendicular lines, such that:

`m_1*m_2 = -1`

You need to convert the given form of each equation in the slope intercept form, `y = m*x + b` , to evaluate the slopes, such that:

`x + 4y = 11 => 4y = -x + 11 => y = -x/4 + 11/4 => m_1 = -1/4`

`4x = y + 21 => y = 4x - 21 => m_2 = 4`

Replacing `-1/4` for `m_1` and 4 for `m_2` in equation `m_1*m_2 = -1 ` yields:

`-1/4*4 = -1 => -1 = -1`

**Hence, evaluating the slopes of the lines and replacing its values in equation `m_1*m_2 = -1` , the equation holds, thus, the lines `D_1` and `D_2` are orthogonal.**

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