Linear Equation and Inequalities

Which three inequalities defines the unshaded white region on the graph?

• x ≥ 1,   

  y ≥ x,  

  x + y < 6

• x ≥ -1,   

  y ≥ x,  

  y < x + 6

• x ≤ 1,   

  y ≤ x,  

  x + y < 6

• x ≥ 1,   

  y ≥ x,  

  x + y > 6

Find the three inequalities which define the unshaded region on the graph.

• x ≥ -2,

    2y > x - 2,  

  y < -2x + 4

• x > -2,

    2y > x - 2,  

  y ≤ -2x + 4

• x ≥ -2,

    2y > x - 1,  

  y < -2x + 4

• x ≥ -2,

    2y > x - 2,  

  y < 2x + 4

Find the equation of a straight line that passes through the points G(-2, 5) and H(3, 15).

• y - 2x = 9

• 5y = 10x - 45

• y + 2x = 9

• 5y + 10x = - 45

A straight line that passes through T(3, 1) and U(7, b) has a gradient of 5.

Find the value of b.

• 21

• 5

• 20

• 22

Find the gradient and y-intercept of the line equation 4x + 3y = 12

• gradient = - 4/3

  y-intercept = 4

• gradient = 4/3

  y-intercept = 4

• gradient = - 4/3

  y-intercept = 12

• gradient = 4/3

  y-intercept = 12

Find the midpoint of a line P(3, 5) and Q(-7, -5)

• (-2, 0)

• (2, 5)

• (-2, 5)

• (2, 0)

Find the equation of the line passing through (-3, -1) and (-5, 7)

• y = - 4x - 13

• y = 4x - 13

• y = - 4x + 13

• y = 4x + 13

Find the line equation of AB in simplest form.

• y = -2x + 4

• y = 2x + 4

• y = -2x + 6

• y = -2x - 2

From the diagram, find:

(a) gradient of AB

(b) line equation of AB

(c) If point (3k, k) lies on the line AB, find k.

• m = 2

  y = 2x - 5

  k = 1

• m = 2

  y = 2x - 7

  k = 2

• m = 2

  y = 2x - 5

  k = 3

• m = 2

  y = 2x + 5

  k = 1

Solve, algebraically the in-equation

3x < 6(x-1) - 12

• x > 6

• x < 6

• x > 18

• x > 9