Line x passes through (2,3) and (7, -1). Line y passes through (5, 4) and (-3,2). Which line is steeper, x or y?

Line x is steeper.
Line y is steeper.
Both a and b
None

hint Hint:

To find which line is steeper we need to find the slope of both lines first. Then we will compare the absolute values of the slopes, the line having greater slope will be the steeper line.

The correct answer is: Line x is steeper.

Given, Line x passes through (2,3) and (7, -1).
Slope $equals fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction equals fraction numerator negative 1 minus 3 over denominator 7 minus 2 end fraction equals fraction numerator negative 4 over denominator 5 end fraction$
Line y passes through (5, 4) and (-3,2).
Slope = $equals fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction equals fraction numerator 2 minus 4 over denominator negative 3 minus 5 end fraction equals fraction numerator negative 2 over denominator 8 end fraction equals 1 fourth$
As we know, greater the absolute value of the slope steeper the line and vice versa.
Now, $4 over 5 greater than 1 fourth$
So line x is steeper.

If l || m then find the measures of x and y?

In this question we have to find x and y given that l is parallel to m and t is the transversal. First to find x we can use linear pair as we know that the sum of angles which are in linear pair is 180 deg. Next to find y we can use the theorem alternate exterior angles are equal.