perpendicular to graph of 3x - 2y = 24, intersects that graph at its x-intercept. Graph the line that satisfies each set of conditions.

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Chapter 2, 2.3 - Problem 49 - Glencoe Algebra 2 (1st Edition, McGraw-Hill Education).
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kspcr111 | In Training Educator

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Given a line `3x - 2y = 24`

we need to find a line which is perpendicular to the line `3x - 2y = 24` and passes through the x- intercept of the line 3x - 2y = 24

let us first find the slope of the line `3x - 2y = 24`

so, getting the line in the standard form as follows

`3x - 2y = 24`

=> `-2y = 24 -3x`

=> `2y = 3x -24`

=> `y = (3/2)x - 24/2`

=> `y=(3/2)x - 12`

so the slope of the line `3x - 2y = 24`  ``is  `m_1 = 3/2`

let the slope of the line which we need to find be `m_2`

as the product of the slopes of perpendicular lines is `-1`

so the equation is given as

`(m_1)(m_2) = -1`

=> `(3/2)(m_2) = -1`

=> `m_2 = -2/3`

 now let us find the x- intercept of the line`3x - 2y = 24`

x- intercept(y=0)

`3x- 2(0) = 24`

=> `3x = 24`

=>` x = 8`

so the desired line which we wanted passes through the point `(8,0)` and the slope of the line is `-2/3`

so the equation of the line is 

`y = (-2/3)x +c`

=> as it passes through `(8,0)` so,

`0 =(-2/3)(8) +c`

=> `c= 16/3`

so the equation of the line is `y = (-2/3)x + 16/3`

the graph is plotted as below

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