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.
-5,6;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.)
The slope of the given line is 1/5. The slope of a line perpendicular to this line would be the negative reciprocal of 1/5, which is -5.
Using the point-slope form of a linear equation, we have:
y - y1 = m(x - x1),
where (x1, y1) is the given point and m is the slope.
Substituting (x1, y1) = (-5, 6) and m = -5, we get:
y - 6 = -5(x - (-5)).
Simplifying the equation:
y - 6 = -5(x + 5).
Expanding the bracket:
y - 6 = -5x - 25.
Rearranging the equation into slope-intercept form:
y = -5x - 19.
Therefore, the equation of the line that passes through (-5, 6) and is perpendicular to y = 1/5x - 2 is y = -5x - 19.