## 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: $$y=-\frac{1}{10}x-99$$$
$$y=-\frac{1}{10}x-99$$\$

Similar Problems from FE Section: Straight Line