I am working on my final project. I do not understand how to determine whether the lines are parallel, perpendicular, or neither
y = 5( 4x + 9) and y = - 1/20x - 4
I know that the formula is y=mx+b but I do not understand.
To determine whether two lines are parallel, perpendicular, or neither, you need to compare their slopes.
In the equation y = mx + b, 'm' represents the slope of the line. For two lines to be parallel, their slopes must be equal. For two lines to be perpendicular, the product of their slopes must be -1. If their slopes are neither equal nor the negative reciprocal of each other, the lines are neither parallel nor perpendicular.
Let's calculate the slope of each line in your example:
For the first line, y = 5(4x + 9):
By comparing this equation with y = mx + b, we can see that the slope 'm' is equal to 20, obtained by multiplying 5 and 4.
For the second line, y = -1/20x - 4:
Comparing this equation with y = mx + b, we can determine that the slope 'm' is -1/20.
Now, we can compare the slopes.
The slope of the first line is 20, and the slope of the second line is -1/20. These slopes are not equal, nor are they the negative reciprocal of each other. Therefore, the lines represented by the equations y = 5(4x + 9) and y = -1/20x - 4 are neither parallel nor perpendicular to each other.