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
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` .