Straight Line Equation
If a straight line passes through point (12, -5) and is perpendicular to y=2x-5, 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,
$$y=2x-5$$
, the slope is 2. Slopes of perpendicular lines are the negative reciprocals of each other, meaning the unknown straight line has a slope of -1/2. The starting equation:
$$$y=-\frac{1}{2}x+b$$$
Because the unknown equation passes through the point (12, -5), let’s substitute those coordinates:
$$$-5=-\frac{1}{2}(12)+b$$$
Solving for
$$b$$
:
$$$b=-5+\frac{1}{2}(12)=-5+6=1$$$
Because the point where the straight line passes through the y-axis is now known, the final equation is:
$$$y=-\frac{1}{2}x+1$$$
$$$y=-\frac{1}{2}x+1$$$
Time Analysis
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