To find the equation of the perpendicular line, we need to first determine the slope of the given line.
The given equation is in slope-intercept form (y = mx + b) where the coefficient of x represents the slope of the line. In this case, the slope is 1/5.
Since the line we are trying to find is perpendicular to the given line, the slopes of the two lines are negative reciprocals of each other.
The negative reciprocal of 1/5 is -5/1 or simply -5.
Now, we can use the point-slope form of a linear equation to find the equation of the perpendicular line:
y - y₁ = m(x - x₁)
where (x₁, y₁) is the given point and m is the slope of the line.
Plugging in the values, we have:
y - 8 = -5(x - (-5))
y - 8 = -5(x + 5)
y - 8 = -5x - 25
y = -5x - 17
Therefore, the equation of the perpendicular line in slope-intercept form is y = -5x - 17.
Write an equation in slope-intercept form of the line that passes through the given point and is perpendicular to the graph of the given equation.
(-5;8); y= 1/5x-2
Write an equation for the perpendicular line in slope-intercept form.
(Simplify your answer. Use integers or fractions for any numbers in the equation.)
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