HSPA wrote:if y is the angle between a line and X-axis then tan y is the line's slope... if y is more tan y is more
Steeper means more y so slope = tan y = more
Apart from above problem:
Do you have a question or doubt
An unclear question is not a doubt
Lines n and p lie on the xy plane. Is the slope of line n less than slope of line p
(1) Lines n and p intersect at (5, 1)
(2) The y-intercept of line n is greater than the y intercept of p
Statement 1 tells us where the lines intersect, but tells us nothing about either of the lines' slopes. If you draw a picture of two lines intersecting at (5,1), you can see that with the information given, we could label either one n. We could make the one with greater slope n, or the one with less slope n. So, we don't have enough information from statement 1.
Now let's consider statement 2, that says that the y intercept of n is greater than that of the y intercept of p. The slopes could be unequal (think about intersecting lines), or we could have parallel lines, in which case the slopes are equal. So, statement 2 is not sufficient on its own.
Now let's consider the statements together. The lines intersect at (5,1), and n has the higher y intercept. Let's look at 3 cases:
1) Both have y intercepts above y=1
Since n intersects higher, then we know n had further to descend, so its slope is steeper (but more negative) than p's. Thus, p has a greater slope.
2) n has intercept above y=1, p has intercept below
n would have a negative slope and p a positive, so p has a greater slope
3) Both have y intercepts below y=1
Both have positive slopes, but p has further to ascend. Thus, p has a greater slope.
