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.)
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.