Answer:
y = 1/4x - 2
Step-by-step explanation:
Line whose perpendicular which we have to find : 8x+2y=14
A line which is in the form of ax + by = c
has slope - a / b
Thus slope for 8x+2y=14 is -8/2 = -4.
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Slope of two lines with slope m1 and m2 which are perpendicular to each other have the slope relation as
m1*m2 = -1.
here m1 is -4. we have to fine m2
thus
-4*m2 = -1
=> m2 = -1/-4 = 1/4
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Equation of slope intercept form line is y = mx + c
c is the intercept of line on y axis
and m is the slope of line.
Thus required line has equation
y = mx + c
m we have calculated as 1/4
thus
y = 1/4x + c
Given that this line passes through (−4,−3). Hence, this point will satify the equation y = 1/4x + c.
Substituting value of x and y with coordinates we have (−4,−3)
-3 = (1/4) * (-4) + c
-3 = -1 + c
=> c = -3 + 1
=> c = -2
y = 1/4x + c , substituting the value c calculated
y = 1/4x - 2
Thus , equation of line perpendicular to the line 8x+2y=14 and passing through point (−4,−3) is y = 1/4x - 2.
or 
or -1