determine wether the following lines are parallel, perpendicular or neither.
y=20x+45 and y=-1/20x+81
they are perpendicular right?
m = slope = 20
m' = slope = -1/20
if m' = -1/m they are perpendicular all right
To determine whether the given lines are parallel, perpendicular, or neither, we need to compare their slopes.
The equation of a line in slope-intercept form is y = mx + b, where "m" is the slope of the line.
In the first equation, y = 20x + 45, the slope (m1) is 20.
In the second equation, y = -1/20x + 81, the slope (m2) is -1/20.
If two lines are parallel, their slopes must be equal. So, to check for parallel lines, we compare the slopes (m1 and m2).
If two lines are perpendicular, their slopes are negative reciprocals of each other. In other words, multiplying the slopes together should give us -1.
Let's compare the slopes:
m1 = 20
m2 = -1/20
Since multiplying m1 and m2 does not give us -1, the lines are not perpendicular.
Therefore, the lines y = 20x + 45 and y = -1/20x + 81 are neither parallel nor perpendicular.