## Straight Line Equation

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

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