58.8k views
5 votes
Are these parallel, perpendicular, or neither y= --2x+4 and -5x+10y=5

NEED HELP ASAP!!!!

User Lavonda
by
8.9k points

1 Answer

6 votes
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
User Eyettea
by
7.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories