GMAT Official Guide Quantitative Review 2019_ Book

GMAT® Official Guide 2019 Quantitative Review

• 4 - 3 - 2

y

(- 2,4) S

4

3

• 1^0
  
  
  • 1
  
  
  • 2
  
  
  • 3
  
  
  • 4
    -5
  
  
  
  

1 2 3 4 X

(3,-3)

The slope of this line is -\-^4 ) = -^7 , so an equation of this line can be found using the point (3,-3)

as follows:^3 - -^2 5

y-(-3)=-f(x-3)

7 21

y+3=-sx+5

y = - - x +-^7 6

5 5

They-intercept is 1. The x - intercept can be found as follows:

0=--^7 x+-^6

5 5

-x^7 = -^6

5 5

x=-^6

7

Both of these intercepts can be seen on the graph.

If the slope of a line is negative, the line slants downward from left to right; if the slope is positive, the

line slants upward. If the slope is 0, the line is horizontal; the equation of such a line is of the form y = b

since m = 0. For a vertical line, slope is not defined, and the equation is of the form x = a, where a is the

x-intercept.

There is a connection between graphs oflines in the coordinate plane and solutions of two linear

equations with two unknowns. If two linear equations with unknowns x and y have a unique solution,

then the graphs of the equations are two lines that intersect in one point, which is the solution. If the

equations are equivalent, then they represent the same line with infinitely many points or solutions. If

the equations have no solution, then they represent parallel lines, which do not intersect.