Lesson 3 Too Big or Not Too Big, That Is the Question Solidify Understanding

Ready

Identify which of the given points are solutions to the following linear equations. There are multiple solutions for each equation.

1.

$3 x + 2 y = 12$

A.

$(2, 4)$

B.

$(3, 2)$

C.

$(4, 0)$

D.

$(0, 6)$

2.

$5 x - y = 10$

A.

$(2, 0)$

B.

$(3, 0)$

C.

$(0, - 10)$

D.

$(1, 1)$

3.

$- x + 6 y = 10$

A.

$(- 4, 1)$

B.

$(- 22, - 2)$

C.

$(2, 2)$

D.

$(10, 0)$

Fill in the value that will make each ordered pair a solution for the given equation.

4.

$x + y = 6$

a.

$(2, \underset{―}{})$

b.

$(0, \underset{―}{})$

c.

$(\underset{―}{}, 0)$

5.

$2 x + 4 y = 8$

a.

$(2, \underset{―}{})$

b.

$(0, \underset{―}{})$

c.

$(\underset{―}{}, 0)$

6.

$3 x - y = 8$

a.

$(2, \underset{―}{})$

b.

$(0, \underset{―}{})$

c.

$(\underset{―}{}, 0)$

Set

Graph each function. Classify the form of each linear equation as slope-intercept, standard, or point-slope.

7.

$3 x + 5 y = 23$

Form:

8.

$f (x) = - 5 x + 7$

Form:

9.

$g (x) = 15 x - 9$

Form:

10.

$f (x) = 2 (x - 5) + 12$

Form:

11.

$- 5 x + 8 y = 37$

Form:

12.

$y = - 7 (x + 3) + 4$

Form:

A line connected to each linear inequality is graphed to divide the plane into two half planes. Test points on each side of the line to determine which half plane contains all of the solutions and then shade the half plane containing the solutions.

13.

$y \leq 3 x + 4$

14.

$y < 7 x - 2$

15.

$y > \frac{- 3}{5} x + 2$

16.

$y \geq - 6$

Go

Solve each inequality and graph the solution set on the number line.

17.

$16 \leq 3 x + 4$

Solution:

18.

$- 37 < 7 x - 2$

Solution:

19.

Why are inequalities like the last two problems graphed on a number line while the ones in the Set portion of this assignment are graphed on a coordinate plane? What difference is there between the inequalities in the last two problems and the ones found in problems 13—16?