## Straight Line Equation

If a straight line passes through point (12, -5) and is perpendicular to y=2x-5, what is its equation?

##
__
__**Hint**

**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,
$$y=2x-5$$
, the slope is 2. Slopes of perpendicular lines are the negative reciprocals of each other, meaning our unknown straight line has a slope of -1/2. We can start off our equation:

$$$y=-\frac{1}{2}x+b$$$

Because we know our unknown equation passes through the point (12, -5), we can substitute those coordinates:

$$$-5=-\frac{1}{2}(12)+b$$$

Solving for
$$b$$
:

$$$b=-5+\frac{1}{2}(12)=-5+6=1$$$

Now that we determined where the straight line passes through the y-axis, we've found our equation:

$$$y=-\frac{1}{2}x+1$$$

$$$y=-\frac{1}{2}x+1$$$