## Parallel Line

If a straight line passes through point (1, 0) and is parallel to y=x, 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 parallel line, $$y=x$$ , the slope is 1. Slopes of parallel lines have identical slopes, meaning the unknown straight line has a slope of 1. The starting equation:
$$y=(1)x+b$$$Because the unknown equation passes through the point (1, 0), let’s substitute those coordinates: $$0=(1)(1)+b$$$
Solving for $$b$$ :
$$b=-(1)(1)=-1$$$Because the point where the straight line passes through the y-axis is now known, the final equation is: $$y=x-1$$$
$$y=x-1$$\$

Similar Problems from FE Section: Straight Line