Lesson: x-intercepts and y-intercepts

Comment on x-intercepts and y-intercepts

Hi Brent,

Sorry, I am struggling to understand your explanation for below question

https://gmatclub.com/forum/in-xy-coordinate-plane-lines-j-and-k-intersect-at-the-point-242317.html


Statement 1: The slope of line k is greater than the slope of line j.

Case a: the slope of line j is positive

Notice that, if line k has a greater slope, then the y-intercept of line j IS greater than the y-intercept of
line k

I didn't understand above. Can you explain with co-ordinate or e.g.
gmat-admin's picture

Link: https://gmatclub.com/forum/in-xy-coordinate-plane-lines-j-and-k-intersec...

Glad to help!

Notice that, on the first diagram, there is 1 blue line and 3 red lines. Let's IGNORE the bottom two red lines, and focus all of our attention on the red line that has its y-intercept just below the blue line.

The blue line is line j, and the one red line is line k

Let's say the Y-INTERCEPT of line j is -3, which means the blue line passes through the point (0, -3)
Let's also say the Y-INTERCEPT of line k is -4.

Okay, now recognize that the SLOPE of line k (red line) is greater than the SLOPE of line j (blue line).
At the same time, the Y-INTERCEPT of line k (red line) is less than the Y-INTERCEPT of line j (blue line), since -4 is less than -3.

Does that help?

Cheers,
Brent

Brent,

I need help working a question where I am finding the area of a triangle on a xy coordinate plane. The coordinates are (0,3) (7,4) and (4,0). Thank you.
gmat-admin's picture

Happy to help!
You'll find my solution here: https://gmatclub.com/forum/in-the-rectangular-coordinate-system-above-th...

Cheers,
Brent

gmat-admin's picture

Happy to help!
You'll find my solution here: https://gmatclub.com/forum/in-the-rectangular-coordinate-system-above-th...

Cheers,
Brent

ari.banerjee's picture

Hi Brent,

Could you please explain the answer to the following qs? I dint understand the explanations provided on the gmat club forum.

In the xy-plane, lines k and l intersect at the point (1,1). Is the y-intercept of k greater than the y-intercept of l?

(1) The slope of k is less than the slope of l.
(2) The slope of l is positive.

Thank you!

Hi Brent,

Have no clue what are they even asking in this question: https://gmatclub.com/forum/how-many-integral-values-of-k-are-possible-if-the-lines-3x-110650.html
gmat-admin's picture

This question is way too time-consuming to be a legit GMAT question.
Nevertheless, here's my solution: https://gmatclub.com/forum/how-many-integral-values-of-k-are-possible-if...

Cheers,
Brent

Hi Brent,

I'm still a bit confused as to what are the x and y intercepts in the equation form: y = mx + c. Please help. Thank you!
gmat-admin's picture

When the equation of a line is written in slope y-intercept form, y = mx + c, we can automatically see what the slope and y-intercept are.
m = slope of the line and b = y-intercept

So, the line defined by the equation y = 2x + 7 has a slope of 2 and a y-intercept of 7.

HOWEVER, in order to find the x-intercept of the line, we'll need to do a bit of work.

When it comes to finding the x-intercept, we must recognize that the x-intercept has ZERO as its y coordinate.

EXAMPLE
Let's find the x-intercept of the line y = 2x + 7
Plug in y = 0 to get: 0 = 2x + 7
Solve, to get: x = -3.5
So, the coordinates of the x-intercept are (-3.5, 0)

The video lesson that covers slope y-intercept form is here: https://www.gmatprepnow.com/module/gmat-algebra-and-equation-solving/vid...

Does that help?

Cheers,
Brent

Hi Brent,

Need your help:

https://gmatclub.com/forum/if-perpendicular-lines-m-and-n-intersect-at-0-b-in-the-161853.html

https://gmatclub.com/forum/in-the-xy-plane-lines-k-and-l-intersect-at-the-point-1-1-is-the-y-218971.html

The solution here says that slope is higher, so the value of y is greater. However, slope would be higher even if the value of x is lesser right?
gmat-admin's picture

Question link: https://gmatclub.com/forum/in-the-xy-plane-lines-k-and-l-intersect-at-th...

I think I agree with you. When you say "the value of x is lesser," are you referring to the x-intercept?

That said, the target question is asking about the y-intercept.

Does that help?

Cheers,
Brent

Hi Brent,

Can you, please, check if my logic is correct on the following question https://gmatclub.com/forum/in-the-x-y-coordinate-plane-does-line-k-have-a-positive-x-intercept-279430.html

Rephrasing the question: Let X intercept be (x,0) where y=0 and let line k formula be y=mx+c 0=mx+c ==> mx=-c ==> x=-c/m is x>0?

Statement 1) Let y-intercept be (0,y) ==> x=0, then y=m*0+c ==> y=c
Per statement 1 (Slope of line k)(y-intercept of line k)>0, we can rewrite as m*y>0 or since y=c we can rewrite m*c>0, if m*c>0, then m/c, or c/m will also be positive (since either both c and m are negative or both c and m are both positive). Hence we know that c/m is definitely positive and thus x=-c/m will definitely be negative, hence x-intercept is negative. Sufficient.

Thanks!
gmat-admin's picture

Question link: https://gmatclub.com/forum/in-the-x-y-coordinate-plane-does-line-k-have-...

That solution is perfectly valid.
ASIDE: For others reading this, Olga is stating that, if the line's equation is y=mx+c, then the x-intercept = -c/m

Cheers,
Brent

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