Lesson: x-intercepts and y-intercepts

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

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

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

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

You bet!
Here you go: https://gre.myprepclub.com/forum/line-k-lies-in-the-xy-plane-the-x-inter...

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...