x+2y=7
2x+4y=5
are the graphs of these equations perpendicular?
2y = -x+7 ---> y = -(1/2) x + 3.5
slope m = -1/2
4y=-2x +5 ---> y = -(1/2) x + 1.25
slope m' = -1/2
the slopes are the same. Therefore they are parallel, not perpendicular.
If they had been perpendicular, you would have found m'=-1/m
To determine if the graphs of two equations are perpendicular, we need to examine the slopes of the lines represented by these equations.
Let's rewrite the equations in slope-intercept form (y = mx + b), where m is the slope:
Equation 1: x + 2y = 7
Rearrange the equation: 2y = -x + 7
Divide by 2: y = (-1/2)x + 7/2
Equation 2: 2x + 4y = 5
Rearrange the equation: 4y = -2x + 5
Divide by 4: y = (-1/2)x + 5/4
By comparing the coefficients of x in both equations, we can see that the slopes are the same (-1/2). Since the slopes are equal, the lines represented by these equations are parallel, not perpendicular.