Write an equation in slope intercept form for the line that passes through (5,-4) and is perpendicular to the line described by 2x-10y=0
To find the equation of a line perpendicular to the given line, we need to determine the slope of the given line first.
Let's rewrite the given equation, 2x-10y=0, in slope-intercept form (y = mx + b):
2x - 10y = 0
-10y = -2x
y = (2/10)x
y = (1/5)x
The slope of this line is 1/5.
The line perpendicular to this line will have a slope that is the negative reciprocal of 1/5, which is -5.
Using the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope, we can substitute the values of m, x1, and y1 with the coordinates of the given point (5, -4) to obtain the equation:
y - (-4) = -5(x - 5)
Simplifying the equation:
y + 4 = -5x + 25
Finally, rewriting the equation in slope-intercept form:
y = -5x + 21