find the slope-intercept equation of the line with the following properties perpendicular to the line x-4y=2; containing the point (5,2)must show work , thank you for the help

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You should remember that the product of the slopes of two perpendicular lines yields -1.

You should put the equation of the given line in slope-intercept form such that:

`-4y = 2 - x => y = x/4 - 2/4 => y = (1/4)x - 1/2`

Comparing this form to general slope intercept form, `y = mx + n` , yields `m = 1/4` .

You need to write the equation that relates the slopes of perpendicular lines such that:

`(1/4)*m_1 = -1 => m_1 = -1/(1/4) => m_1 = -4`

Since the problem provides the information that the line passes through the point (5,2), you need to write the point slope form of equation such that:

`y - 2 = -4*(x - 5)`

You need to open the brackets and to put this equation in slope intercept form isolating the terms that contains y to the left side such that:

`y = -4x + 20 + 2 => y = -4x + 22`

Hence, evaluating the slope intercept form of the equation that follows the given conditions yields  `y = -4x + 22` .

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