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.
(-5,2);y=1/5x-2
The given equation is y = (1/5)x - 2.
First, we need to find the slope of the line that is perpendicular to the graph of this equation.
The slope of the given line is 1/5.
Perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of the line perpendicular to the given line is -5/1, which is -5.
Using the point-slope form of a linear equation, we have:
y - y1 = m(x - x1),
where m is the slope and (x1, y1) is the given point (-5, 2).
Substituting the values, we have:
y - 2 = -5(x - (-5)).
Simplifying:
y - 2 = -5(x + 5).
Expanding:
y - 2 = -5x - 25.
Finally, rearranging the equation into slope-intercept form:
y = -5x - 23.