In the xy-plane, the points (a, 0) and (0, b)

In the xy-plane, the points (a, 0) and (0, b) are on the line whose equation is y = (1/2)(x) + 10. Quantity A: a Quantity B: b Quantity A is greater., Quantity B is greater., The two quantities are equal., The relationship cannot be determined from the information given.

4 Explanations

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Kartik Chandwani

Can I do it with a different method? which is,
(a,0) (0,b)
Y = 1/2x+10
1/2 = b-0 / 0-a
1/2 = b/-a
a= -2 b=1

Apr 19, 2020 • Comment

Adam

This does not work to find the values of a and b. You've found the ratio between them, but this does *not* mean that a = -2. And in fact, an x-value of -2 yields a y-value of 9, meaning that (-2, 9) is on our line, not (-2, 0).

Note as well that a = 2 and b = -1 fits your conclusion also. We have to remember, though, that our slope is positive, and the y-value of our y-intercept is also positive, at (0, 10). This means b is positive, and a is negative, so b is greater.

Apr 24, 2020 • Reply

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That's right :) We have a positive slope and a positive y intercept.

(a,0) is really just where the line crosses the x axis. And we know this is to the left side of the XY plane (to the left of the y axis), so "a" must be negative.

(0,b) is where the line crosses the y axis. But we know this value is 10, which is positive.

Dec 20, 2014 • Comment

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Meera Kibe

Slope =1/2 so positive slope .
Y intercept is 10
A is thus neg if we draw a xy plane therefore

Dec 3, 2014 • Comment

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Chris Lele