Question

lesson 5 practice problems

1. select all the points that are on the graph of the equation 4y - 6x = 12.

a. (-4,-3)
b. (-1,1.5)
c. (0,-2)
d. (0,3)
e. (3,-4)
f. (6,4)

1. here is a graph of the equation x + 3y = 6.

select all coordinate pairs that represent a solution to the equation.
a (0,2)
b(0,6)
c. (2,6)
d. (3,1)
e. (4,1)
f. (6,2)

Explanation:

Step1: Check points for equation $4y - 6x=12$

Substitute the $x$ and $y$ - values of each point into the equation.

For point A $(-4,-3)$

Substitute $x = - 4$ and $y=-3$ into $4y - 6x$:
$4\times(-3)-6\times(-4)=-12 + 24=12$. So point A is on the graph.

For point B $(-1,1.5)$

Substitute $x=-1$ and $y = 1.5$ into $4y - 6x$:
$4\times1.5-6\times(-1)=6 + 6=12$. So point B is on the graph.

For point C $(0,-2)$

Substitute $x = 0$ and $y=-2$ into $4y - 6x$:
$4\times(-2)-6\times0=-8
eq12$. So point C is not on the graph.

For point D $(0,3)$

Substitute $x = 0$ and $y = 3$ into $4y - 6x$:
$4\times3-6\times0=12$. So point D is on the graph.

For point E $(3,-4)$

Substitute $x = 3$ and $y=-4$ into $4y - 6x$:
$4\times(-4)-6\times3=-16-18=-34
eq12$. So point E is not on the graph.

For point F $(6,4)$

Substitute $x = 6$ and $y = 4$ into $4y - 6x$:
$4\times4-6\times6=16 - 36=-20
eq12$. So point F is not on the graph.

Step2: Check points for equation $x + 3y=6$

Substitute the $x$ and $y$ - values of each point into the equation.

For point A $(0,2)$

Substitute $x = 0$ and $y = 2$ into $x + 3y$:
$0+3\times2=6$. So point A is a solution.

For point B $(0,6)$

Substitute $x = 0$ and $y = 6$ into $x + 3y$:
$0+3\times6=18
eq6$. So point B is not a solution.

For point C $(2,6)$

Substitute $x = 2$ and $y = 6$ into $x + 3y$:
$2+3\times6=2 + 18=20
eq6$. So point C is not a solution.

For point D $(3,1)$

Substitute $x = 3$ and $y = 1$ into $x + 3y$:
$3+3\times1=3 + 3=6$. So point D is a solution.

For point E $(4,1)$

Substitute $x = 4$ and $y = 1$ into $x + 3y$:
$4+3\times1=4 + 3=7
eq6$. So point E is not a solution.

For point F $(6,2)$

Substitute $x = 6$ and $y = 2$ into $x + 3y$:
$6+3\times2=6 + 6=12
eq6$. So point F is not a solution.

Answer:

1. A. $(-4,-3)$, B. $(-1,1.5)$, D. $(0,3)$
2. A. $(0,2)$, D. $(3,1)$