- D Since lines l and k are perpendicular, their slopes are negative reciprocals.
Since the slope of line l is 3, the slope of line k is −^13. The equation for line
k now reads: y = −^13 x + b. Since the lines intersect at the point (3,4), those
coordinates must satisfy the equation for line k. To solve for b, plug those
coordinates into the equation:
y = −^13 x + b
4 = −^13 3 + b
4 = −1 + b
5 = b
The equation for line k is thus y = −^13 x + 5. - B Isolate y so that the equation is in y = mx + b form:
ax + by = c
by = −ax + c
y = –ax + cb
y = –bax + cb
The slope of the line is thus −ab. Since the slope of the line is negative,- a
b < 0. Thus
- a
a
b > 0.Quantitative Comparison Questions
- A Since the lines go downward, both slopes are negative. Line m is steeper,
meaning its slope is more negative than the slope of l. Thus the slope of l is
greater. The correct answer is A. - B Since line m contains the points (0,0) and (3,5), its slope is (5 – 0)/(3 − 0) =^53.
Line m is steeper than line l, so the slope of line l must be less than^53 , meaning
its slope is less than 2. The correct answer is B. - C Since line q passes through the origin, it must contain the point (0,0). The
slope of line q is thus b a – 0– 0 = ba. The two quantities are equal. The answer is C. - B The slope of the line is b 0 – – 0d = –bd. Since the line points downward, its slope
must be negative. Thus –bd < 0. Multiply both sides by −1 (remember to flip the
inequality!): bd > 0. Since m < 0 and db > 0, Quantity B is greater. - B Manipulate the equation to be in y = mx + b form:
2 y – 3x + 7 = 12
2 y – 3x = 5
2 y = 3x + 5
y =^32 x +^52
The slope is^32 and the y-intercept is^52. Quantity B is greater.
446 PART 4 ■ MATH REVIEW04-GRE-Test-2018_313-462.indd 446 12/05/17 12:07 pm