Find the slope of a line perpendicular to the line whose equation is x, minus, 2, y, equals, minus, 8x−2y=−8. Fully simplify your answer.
To find the slope of the line with the equation 8x - 2y = -8, we first need to rewrite it in slope-intercept form (y = mx + b), where m is the slope of the line.
8x - 2y = -8
-2y = -8x - 8
y = 4x + 4
Now we can see that the slope of the line is 4.
To find the slope of the line perpendicular to this line, we take the negative reciprocal of the slope of the given line.
Therefore, the slope of the line perpendicular to the line with the equation 8x - 2y = -8 is:
m_perpendicular = -1/4
So, the slope of the perpendicular line is -1/4.