are the following lines parallel, perpendicular or neither 4x+5y=7 5x+4y=10
To determine whether two lines are parallel, perpendicular, or neither, we need to compare their slopes.
The equations of the lines are:
1) 4x + 5y = 7
2) 5x + 4y = 10
Let's rearrange both equations to the slope-intercept form (y = mx + b) where "m” represents the slope:
1) 4x + 5y = 7 => 5y = -4x + 7 => y = (-4/5)x + 7/5
2) 5x + 4y = 10 => 4y = -5x + 10 => y = (-5/4)x + 10/4 => y = (-5/4)x + 5/2
Now we can compare the slopes.
The slope of the first line is -4/5, and the slope of the second line is -5/4.
If two lines are parallel, their slopes are equal. If two lines are perpendicular, their slopes are negative reciprocals (the product of the slopes is -1). Otherwise, if the slopes are neither equal nor negative reciprocals, the lines are neither parallel nor perpendicular.
Let's calculate the product of the slopes:
(-4/5) * (-5/4) = 20/20 = 1
Since the product of the slopes is 1 (not -1), we can conclude that the lines are neither parallel nor perpendicular.
In summary, the given lines 4x + 5y = 7 and 5x + 4y = 10 are neither parallel nor perpendicular.