Parallel lines have equal slopes but different y-intercepts, so they start on different y-axis locations but will never intersect since they have equal gradients (slopes). Perpendicular lines have negative reciprocal slopes. So, let’s transform all equations into slope-intercept form for simplicity.
Equation 1: y=-2x+4 is already in y=mx+b
We must get equation 2 into this form as well.
Equation 2: -5x+10y=5
Add 5x to both sides:
10y=5x+5
Divide by 10 on both sides:
y=5/10x+5/10
Simplify:
y=1/2x+1/2
Let’s look at the slopes of equations 1 and 2.
Equation 1: m=-2
Equation 2: m=1/2
Notice that 1/2 is the negative reciprocal of -2, since -(-1/2)=1/2
Therefore, the lines are perpendicular