Thread: How would you determine the equation of a parallel or perpendicular line and a point on the new line?

I understand that the slopes of parallel lines are equal and the slopes of perpendicular lines are the opossite reciprocal, but like I said in the question above, I'm confused on how you could write out an equation for the new parallel or perpendicular line and be able to provide a point. Could anyone help me? Thanks.

y = 2x + 2 and (2, 2)

To find the parallel line that is parallel to y = 2x + 2 and goes through the point (2, 2), you need to plug in given points into the given equation with the y-intercept as undefined.

ex. 2 = 2(2) + b

By doing this, you'll be able to find the y-intercept of the second line.

2 = 2(2) + b
2 = 4 + b
Subtract 4 from both sides
-2 = b

The equation parallel to y = 2x + 2 and goes through the points (2, 2) is y = 2x - 2

For the perpendicular line, the slope, like you said, is the opposite reciprocal. The y-intercept is the same as the first equation.

y = 2x + 5
y = -1/2x + 5

To provide a point, you could just draw/sketch the line and find the point.