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Comment on x-intercepts and y-intercepts
could you please help me
(http://gre.myprepclub.com/forum/in-the-xy-plane-line-k-is-a-line-that-does-not-pass-throug-1842.html)"?
"A) The x-intercept of line k is twice the y-intercept of line k." does not make sense to me.
Glad to help.
Glad to help.
I agree; the concept is somewhat strange, certainly not something one typically uses on a regular basis :-)
Please go to 2:30 in the above video and take a look at the line.
First notice that it crosses the y-axis at the point (0, 1.5). So, we say that the line has a y-intercept of 1.5
Also notice that it crosses the x-axis at the point (2, 0). So, we say that the line has an x-intercept of 2
In this case, the x-intercept of the line is 4/3 times the y-intercept of the line (since 2 = (4/3)(1.5).
-----------------------------------------------------
If, for example, a line has an x-intercept of 6 [i.e., the line crosses the x-axis at the point (6, 0)] and a y-intercept of 3 [i.e., the line crosses the y-axis at the point (0, 3)], then we could say that the x-intercept of the line is TWICE the y-intercept of the line (since 6 is twice as big as 3).
Does that help?
Cheers,
Brent
THANK you, Brent! Eventually
I am sorry for this late response. My idea was that it was the best for me to get away from this question and revisit it after clearing my head. It enabled me to approach this question from your close direction to finally get it.
I am grateful to you for your close direction!
S
Hi Brent,
I still don't understand the solution given.Its written the intercepts having the same sign have negative slopes .Could u please explain this?
http://gre.myprepclub.com/forum/in-the-xy-plane-line-k-is-a-line-that-does-not-pass-throug-1842.html
Happy to help!
Happy to help!
The x-intercept can be either positive or negative, and the y-intercept can be either positive or negative.
The solution basically says...
If the x-intercept and y-intercept of a line are both POSITIVE, then the slope of the line will be negative. Likewise, if the x-intercept and y-intercept of a line are both NEGATIVE, then the slope of the line will be negative. In other words, if the x-intercept and y-intercept have the SAME SIGN (both positive or both negative), then the slope of the line will be negative.
To see why this is true, get some paper and sketch some possibilities.
CASE A: Let's first try the case where the x-intercept and y-intercept of a line are both POSITIVE.
Let's say the x-intercept is 2 (or any other positive value you choose) and the y-intercept is 5 (or any value YOU choose).
Now draw an xy plane, and add the points (2,0) and (5,0) to denote the x-intercept and y-intercept,
When you draw the line through those two points, you'll get a line with a negative slope.
CASE B: Let's first try the case where the x-intercept and y-intercept of a line are both NEGATIVE.
Let's say the x-intercept is -3 and the y-intercept is -1 (or any negative values YOU choose).
Now draw an xy plane, and add the points (-3,0) and (-1,0) to denote the x-intercept and y-intercept,
When you draw the line through those two points, you'll get a line with a negative slope.
Does that help?
Cheers,
Brent
https://gre.myprepclub.com/forum
Please how did we get she get the values of a and b in the explanation given below
We know that every single line in 2D has a formula: y=ax+b
This line goes through 2 points A(x1,y1),B(x2,y2) which means if we input x1 in the above formula we will have y1.
Then we have 2 equations for 2 unknowns a and b: 33=48a+b and 22=31a+b. Solve for a and b to have y=(11/17)*x+33/17
X-intercept means that the point intercept between the line and Ox which means y=0 then solve for x=-3
Question link: https:/
Question link: https://gre.myprepclub.com/forum/if-line-k-passes-through-the-points-48-...
In that solution, tuankhanh21 is finding the equation of the line (in slope y-intercept form).
Once we know the equation of the line, we can find the x-intercept.
Here's the video on finding the equation of the line (in slope y-intercept form): https://www.greenlighttestprep.com/module/gre-algebra-and-equation-solvi...
Cheers,
Brent
Hi Brent,
https://gre.myprepclub.com/forum/if-the-equation-y-3x-18-were-graphed-on-the-coordinate-a-12106.html
in thsi even option D is also true'
given x = 6 and y = 0
y=3x-18
0=3(6)-18
0=0
so why didnt we consider it could you please explain me
Thanks
You're correct to say that
You're correct to say that the pair of values, x = 6 & y = 0, satisfies the given equation, which means the point (6,0) lies on the line.
However, we need to find the point where the line crosses the y-axis, and (6,0) is not on the y-axis (it is, however, on the x-axis)
Cheers,
Brent
https://gre.myprepclub.com/forum
Could you solve this please!
Thanks
You bet!
You bet!
Here you go: https://gre.myprepclub.com/forum/line-k-lies-in-the-xy-plane-the-x-inter...
https://gre.myprepclub.com/forum
How is 0 = √x + 1 unsolvable for x? We can square both sides and get x=1?
x = 1 isn't a solution to the
x = 1 isn't a solution to the equation 0 = √x + 1.
We can show this by plugging x = 1 into the equation to get: 0 = √1 + 1
Simplify: 0 = 2 (doesn't work)
Alternatively, we can take the equation 0 = √x + 1
Subtract 1 from both sides to get: -1 = √x
Since the square root NOTATION tells us to take the non-negative square root of a value, we can conclude that the equation -1 = √x is unsolvable.
Important: When solving equations involving a variable inside the square root sign, we must always check for extraneous roots.
Related lesson: https://www.greenlighttestprep.com/module/gre-algebra-and-equation-solvi...