46. Are the graphs of the equations below parallel, perpendicular or neither? y=2/5x+3 and y=3/5x-4 Explain.
y = m x + b
where m is the slope
the first m = 2/5
the second m = 3/5
Two different slopes.They will run into each other, not parallel
Now if perpendicular
m' = -1/m
does
3/5 = - 5/2
I think not.
You are welcome.
I already know it's neither I just don't know how to explain.
Thank you!
To determine whether the graphs of two linear equations are parallel, perpendicular, or neither, we need to compare their slopes.
First, let's write the equations in slope-intercept form (y = mx + b), where "m" represents the slope:
Equation 1: y = (2/5)x + 3
Equation 2: y = (3/5)x - 4
By comparing the coefficients in front of the x-term, we can determine the slopes of the two lines:
The slope of Equation 1 is 2/5.
The slope of Equation 2 is 3/5.
Since the slopes (2/5 and 3/5) are different but not negative reciprocals of each other, the graphs of the two equations are neither parallel nor perpendicular.
In general, two lines are parallel if and only if their slopes are equal. Therefore, since the slopes are not equal in this case, the lines are not parallel.
Two lines are perpendicular if and only if the product of their slopes is -1. In this case, the product of the slopes (2/5 and 3/5) is not equal to -1, so the lines are not perpendicular.
Conclusion: The graphs of the equations y = (2/5)x + 3 and y = (3/5)x - 4 are neither parallel nor perpendicular.