Thank you for the opportunity to help you with your question!
Hey, Kaylee! I would love to answer this question for you. Can you send me a picture of the image your teacher gave you (where the blue line is, etc.). I can get you your answer in about two minutes once I have that information. Thanks!Please let me know if you need any clarification. I'm always happy to answer your questions.
Lets say you need a slope intercept equation for a line that goes through (-2,1) and is perpendicular to y= 5. y= 5 has a slope of zero. So, to find the line perpendicular, we need to draw y=5 (straight horizontal line) and plot the point (-2,1). Since the line is perpendicular to y=5, it must be vertical. This vertical line must also pass through (-2,1). So, we know the line will pass through all points where x = -2. Because it will always pass through x = -2, you can only write a simple equation of x = -2
Thanks, Kaylee. Give me just a little bit to compute it!
Just a few more minutes, Kaylee. I'm trying to type it out very detailed and the "Common core" way for you so you receive all of the points. :)
So, for A you were on the right track...I think you just missed one step!
For PARALLEL LINES, the slope is the same! So to find the slope, we need to find two points. I picked the points (-2,1) and (0,-3)
to find the slope we use the equation m = (y1-y2)/(x1-x2) or we can just look at the graph. For every 2 boxes we go down (Y) we move over one box (x). So, our slope would be -2
Next, we know the points the parallel line goes through are (3,5). We know need to use the point slope equation which is:
Plugging in our numbers we get:
Now lets distribute -2 through the right hand side. This gives us Y-5 = -2x+6
Now, we need to add 5 to both sides. once we do this, we get Y = -2x +11.
So the answer for number 1 is Y = -2x +11
Now, for perpendicular, we know that the slope is the negative inverse of the slope of the line given.
To find slope, lets take two points (0,2) and -(2,1) When we use the equation m = (y1-y2)/(x1-x2) we can plug it in to be (2-1)/(0-(-2) which gives us a slope of the line as 1/2.
Now to find the negative inverse, we need to divide 1 by 1/2 (1/(1/2) or 1/.5 = 2. Then we need to multiply it by -1. so 2*-1 = -2 . So our slope for the perpendicular line is -2.
Now, we just plug it into y-y1= m(x-x1)with the points given (4,0)
Multiply -2 across and we get y= -2x +8 <--- ANSWER.
Content will be erased after question is completed.