Option 2: [tex]y = -\frac{8}{7}x-\frac{18}{7}[/tex] is the correct answer
Step-by-step explanation:
Given equation of line is;
[tex]y = \frac{7}{8}x-\frac{3}{2}[/tex]
Let m1 be the slope of given line
As the equation of line is in slope-intercept form, the coefficient of x will be the slope of the line
[tex]m_1= \frac{7}{8}[/tex]
As we know that product of slopes of two perpendicular lines is -1
Let m2 be the slope of the line perpendicular to given line
So,
[tex]m_1.m_2= -1\\\frac{7}{8}.m_2= -1\\m_2 = -1 * \frac{8}{7}\\m_2= -\frac{8}{7}[/tex]
Th equation of line is:
[tex]y = m_2x+b[/tex]
Putting the value of m2
[tex]y = -\frac{8}{7}x+b[/tex]
Putting the point (-4,2) in the equation
[tex]2 = -\frac{8}{7}(-4)+b\\2 = \frac{32}{7}+b\\2 - \frac{32}{7} = b\\\frac{14-32}{7} = b\\b = -\frac{18}{7}[/tex]
Putting the value of b in the equation
[tex]y = -\frac{8}{7}x-\frac{18}{7}[/tex]
Hence,
Option 2: [tex]y = -\frac{8}{7}x-\frac{18}{7}[/tex] is the correct answer
Keywords: Equation of line, slope
Learn more about equation of line at:
- brainly.com/question/2586096
- brainly.com/question/2568692
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