Passes through (2, -5), perpendicular to the graph of y = 1/4 x + 7. Write an equation in slope-intercept form for the line that satisfies each set of conditions.

Textbook Question

Chapter 2, 2.4 - Problem 36 - Glencoe Algebra 2 (1st Edition, McGraw-Hill Education).
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kspcr111 | In Training Educator

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Given an equation of a line L1 is y = 1/4 x + 7

y = 1/4 x + 7

so the slope of the line L1 be m_1 is = 1/4

as we know that the product of the  slopes of the two perpendicular lines is equal to -1

let the slope of the required line is m_2

so ,

(m_1)(m_2) = -1

=> m_2 = -4

As,the slope-intercept form of  the required line is

`y= (m_2)x+b`

from the above we know `m_2 = -4` , so the line equation is 

`y= (-4)x+b` --------------(1)

we need to find the value of b , as the line passes through the point

`(x,y)= (2, -5 )` , then on substituting we get

`-5 =(-4)*(2)+b`

=> `b = -5 +8 = 3 `

so the equation of the line is

`y= (-4)x+ 3`

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