The following problems are in slope,point slope, and slope intercept forms of a line.
Could you check these thanks.
Find the slope intercept form of a line that passes through these two points (-4,4) and (2,1)
Answer: y= -1/2x-2
Find the slope intercept form of a line that is parallel to the line created in problem #1 and passes through the point ( -2,6)
Answer: y= -1/2x+4
Find the slope intercept form of a line that is perpendicular to the line created in problem #1 and passes through the point (1,3). What can you say about the relationship of this line and the line created in problem #2.
Answer: y= -1/2x+1/1/2
My response: I can say that is I used the same slope which is -1/2x
two points (-4,4) and (2,1)
m = slope = (Y1-Y1)/(X2-X1)
= (1-4)/(2+4) = -3/6 = -1/2
then put either point in:
y = -(1/2) x + b
1 = -(1/2) 2 + b
1 = -1 + b
b = 2
so
y = -(1/2) x + 2
I think you have a sign error in your answer for b
if parallel, same slope = -(1/2)
y = -(1/2) x + b
now the point in
6 = -(1/2)(-2) + b
6 = 1 + b
b = 5
so
y = -(1/2) x + 5
then perpendicular
m = -1/-(1/2) = 2
s
y = 2 x + b
3 = 2(1) + b
b = 1
so
y = 2 x + 1
By the way, you can always check the answers by seeing if all the points fit the line you come up with.
Thank you very much you really Helped!
I had the same homework to not like this but now I know how to do it thanks chico for posting a similar problem and thanks damon
yo sup peops 2x - is y
-
by - the two numbers and it gives you x or y or w
WHAT THE HECK IS ALLL THIS MESSS
HOW WILL U DO THE MESS I DON'T UNDERSTNAD IT!!!!!!!!! IGUESS
To find the slope-intercept form of a line, you need to use the formula:
y = mx + b
where m represents the slope and b represents the y-intercept.
For Problem #1:
Given the points (-4,4) and (2,1), we can find the slope using the formula:
m = (y2 - y1)/(x2 - x1)
m = (1 - 4)/(2 - (-4))
m = -3/6
m = -1/2
Now that we have the slope (m), we can substitute it into the slope-intercept form and choose any of the given points to solve for b:
1 = (-1/2)(2) + b
1 = -1 + b
b = 1 + 1
b = 2
Therefore, the slope-intercept form of the line passing through (-4,4) and (2,1) is:
y = -1/2x + 2
For Problem #2:
The line in problem #2 is parallel to the line in problem #1, which means they have the same slope. The given point for problem #2 is (-2,6). Using the slope (-1/2) and the point (-2,6), we can solve for b:
6 = (-1/2)(-2) + b
6 = 1 + b
b = 6 - 1
b = 5
Therefore, the slope-intercept form of the line parallel to the line from problem #1 and passing through the point (-2,6) is:
y = -1/2x + 5
For Problem #3:
The line in problem #3 is perpendicular to the line in problem #1. Remember that perpendicular lines have negative reciprocal slopes. Since the slope of the line in problem #1 is -1/2, the slope of the line in problem #3 will be the negative reciprocal, which is 2.
Using the slope (2) and the given point (1,3), we can solve for b:
3 = 2(1) + b
3 = 2 + b
b = 3 - 2
b = 1
Therefore, the slope-intercept form of the line perpendicular to the line in problem #1 and passing through the point (1,3) is:
y = 2x + 1
In summary, the relationship between the line in problem #2 and the line in problem #3 is that they have the same slope (-1/2), but they are not the same line since they have different y-intercepts (4 and 1, respectively).