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Answer:
Equation of line perpendicular to given graph is:
[tex]y = -\frac{1}{2}x+4[/tex]
Step-by-step explanation:
Given equation of line is:
14x-7y=8
First of all, we have to convert the given equation into slope-intercept form to find the slope of the line
The slope-intercept form is:
[tex]y = mx+b[/tex]
Now
[tex]14x-7y=8\\14x-8 = 7y\\\frac{7y}{7} = \frac{14x-8}{7}\\y = \frac{14}{7}x - \frac{8}{7}\\y = 2x - \frac{8}{7}[/tex]
The co-efficient of x is 2 so the slope of given line is 2
Let m1 be the slope of line perpendicular to given line
The product of slopes of two perpendicular lines is -1
[tex]m.m_1 = -1\\2.m_1 = -1\\m_1 = -\frac{1}{2}[/tex]
The equation for line perpendicular line to given line will be:
[tex]y = m_1x+b\\y = -\frac{1}{2}x+b[/tex]
To find the value of b, putting (-2,5) in the equation
[tex]5 = -\frac{1}{2}(-2) + b\\5 = 1+b\\b = 5-1\\b = 4[/tex]
The final equation is:
[tex]y = -\frac{1}{2}x+4[/tex]
Hence,
Equation of line perpendicular to given graph is:
[tex]y = -\frac{1}{2}x+4[/tex]