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4 years ago

Choose the correct graph to fit the equation 3y=2x+4

Mathematics

2 answers:

vfiekz [6]4 years ago

8 0

Answer:

y=2x+1

Step-by-step explanation:

Well, let's start with the graph given by the question. (Picture 1 below)

1) We can pick two points, (1,1) and (-1,-3), also for the slope we can see it's a positive one so m >0

2) $m=\frac{-3-1}{-1-1} \\ m=\frac{-4}{-2}\\ m=2$

So now

y=mx+b

y=2x+b

Plugging in those values (1,1) and (-1,-3)

1=2(1)+b

b=-1

So y=2x-1, instead of 3y=2x+4

bazaltina [42]4 years ago

4 0

Answer:

We need to see a picture of the graphs in order to pick the correct one.

Step-by-step explanation:

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How many Solutions does this system have? (1 point)

mixas84 [53]

The given system of equation that is $2x+y=3$ and $6x=9-3y$ has infinite number of solutions.

Option -C.

<u>Solution:</u>

Need to determine number of solution given system of equation has.

$\begin{array}{l}{2 x+y=3} \\\\ {6 x=9-3 y}\end{array}$

Let us first bring the equation in standard form for comparison

$\begin{array}{l}{2 x+y-3=0} \\\\ {6 x+3 y-9=0}\end{array}$

$\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$

To check how many solutions are there for system of equations $a_{1} x+b_{1} y+c_{1}=0 \text{ and }a_{2} x+b_{2} y+c_{2}=0$ , we need to compare ratios of $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}} \text { and } \frac{c_{1}}{c_{2}}$

In our case,

$a_{1} = 2, b_{1}= 1\text{ and }c_{1}= -3$

$a_{2} = 6, b_{2} = 3,\text{ and }c_{2} = -9$

$\begin{array}{l}{\Rightarrow \frac{a_{1}}{a_{2}}=\frac{2}{6}=\frac{1}{3}} \\\\ {\Rightarrow \frac{b_{1}}{b_{2}}=\frac{1}{3}} \\\\ {\Rightarrow \frac{c_{1}}{c_{2}}=\frac{-3}{-9}=\frac{1}{3}} \\\\ {\Rightarrow \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}=\frac{1}{3}}\end{array}$

As $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$ , so given system of equations have infinite number of solutions.

Hence, we can conclude that system has infinite number of solutions.

5 0

3 years ago

Solve this

sesenic [268]

A sandwich store charges a delivery fee to bring lunch to an office.

Delivery cost - D

Meatball sandwich cost - M

One office pays $40.50 for 5 meatball sandwiches.

40.50 = 5M + D

Another office pays $66.50 for 9 meat ball sandwiches

66.50 = 9M + D

A. How much does each meatball sandwich add to the cost of delivery?

D = 40.50 - 5M = 66.50 - 9M

40.50 - 5M = 66.50 - 9M

9M - 5M = 66.50 - 40.50

4M = 26.00

M = 6.50

B. What is the delivery fee

D = 40.50 - 5M = 40.50 - 5(6.50) = 40.50 - 32.50 = 8.00

Check

66.50 = 9M + D = 9(6.50) + 8 = 58.50 + 8.00 = 66.50

3 0

3 years ago