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.