# Coordinate geometry basic

Two straight lines l and m pass through the point (1,1). Slope of line l passing through the point (0,a) is less than the slope of the line m that passes through the point(0,b).

• Quantity A : a
• Quantity B : b

Options:

• Quantity A is greater than Quantity B
• Quantity B is greater than Quantity A
• Quantity A is equal to Quantity B
• Relationship cannot be determined

If I have envisioned this properly, the figure looks something like this:

I think answer should be B, but it is given as A ie, a>b how is that possible?

• In your image, the line going through $(0,b)$ has slope less than the line going through $(0,a)$. – A. Goodier Jun 16 '18 at 13:45
• @A.Goodier because slope is of negative value, yes? – Shreya Chandwadkar Jun 16 '18 at 14:04
• Yes, that's right – A. Goodier Jun 16 '18 at 14:12

Using the two point form for both lines,

$\frac{y-y_1}{x-x_1} = \frac{y_2-y_1}{x_2-x_1}$

Equation for the lines are:

$y=(1-a)x + a$ for line $l$

$y=(1-b)x + b$ for line $m$

Slope of line $l$ is less than that of $m$:

$1-a < 1-b$

$a > b$

• Better approach, Thanks! :) – Shreya Chandwadkar Jun 17 '18 at 3:01