Is this pair of lines parallel, perpendicular, or neither?
2x+5y=7
5x-2y=8
the slope of the first is -2/5 and the slope of the second is 5/2
notice their product is -1, so they are perpendicular.
(slopes are negative reciprocals of each other)
(to get the slope in my head I used the rule:
for Ax + By = C, slope = -A/B )
Change into the standard equation for a straight line of y = mx + b
2x+5y=7 and
5y = -2x+7 then divide by 5 to obtain
y=(-2/5)x + 7/5
Second equation is
5x-2y=8
-2y=-5x+8
multiply by -1
2y=5x-8
y=(5/2)x-4
Lines are parallel if the slopes are equal. Lines are perpendicular if the slopes are the negative reciprocal of each other.
-
To determine if the given pair of lines is parallel, perpendicular, or neither, we need to compare their slopes.
First, let's rewrite both equations in slope-intercept form (y = mx + b):
2x + 5y = 7
5y = -2x + 7
y = (-2/5)x + 7/5
5x - 2y = 8
-2y = -5x + 8
y = (5/2)x - 4
Now we can compare the slopes:
The slope of the first equation is -2/5, and the slope of the second equation is 5/2.
Since the product of the slopes is not -1 (the condition for perpendicular lines), and the slopes are not equal (the condition for parallel lines), we can conclude that the given pair of lines is neither parallel nor perpendicular.
To determine whether the pair of lines is parallel, perpendicular, or neither, we'll compare their slopes. The standard form of a linear equation is y = mx + b, where m represents the slope.
The given equations are:
1) 2x + 5y = 7
2) 5x - 2y = 8
To find the slope of each equation, we need to rearrange them into the standard form (y = mx + b).
1) 2x + 5y = 7
Rearranging the equation, we get:
5y = -2x + 7
Dividing through by 5, we have:
y = (-2/5)x + 7/5
So, the slope of the first equation is -2/5.
2) 5x - 2y = 8
Rearranging the equation, we get:
-2y = -5x + 8
Dividing through by -2 (or multiplying by -1/2), we have:
y = (5/2)x - 4
So, the slope of the second equation is 5/2.
Since the slopes of the two lines are different (-2/5 and 5/2), the lines are neither parallel nor perpendicular.