## Straight Line

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

##
__
__**Expand Hint**

**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**

**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**

128. Straight Line Equation

131. Two Lines

395. Slope Intercept

396. Point-slope

519. Parallel Line