Straight Line

If a straight line passes through point (2, -100) and is perpendicular to y=10x, what is its equation?

Expand Hint
The standard form of an equation, which is also known as slope-intercept form:
$$$y=mx+b$$$
where $$m$$ is the slope and $$b$$ is the line’s intersection along the y-axis.
Hint 2
Slopes of perpendicular lines are the negative reciprocals of each other. Parallel lines have identical slopes.
The standard form of an equation, which is also known as slope-intercept form:
$$$y=mx+b$$$
where $$m$$ is the slope and $$b$$ is the line’s intersection along the y-axis.

In the given perpendicular line, $$y=10x$$ , the slope is 10. Slopes of perpendicular lines are the negative reciprocals of each other, meaning the unknown straight line has a slope of -1/10. The starting equation:
$$$y=-\frac{1}{10}x+b$$$
Because the unknown equation passes through the point (2, -100), let’s substitute those coordinates:
$$$-100=-\frac{1}{2}(2)+b$$$
Solving for $$b$$ :
$$$b=-100+\frac{2}{2}=-100+1=-99$$$
Because the point where the straight line passes through the y-axis is now known, the final equation is:
$$$y=-\frac{1}{10}x-99$$$
$$$y=-\frac{1}{10}x-99$$$