Which ordered pairs (x,y) are solutions to the linear equation 2x+3y=6
2 answers:
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Answer:
B and C
Step-by-step explanation:
Rearrange each equation into slope- intercept form
A
3x - 2y = 4 ( subtract 3x from both sides )
- 2y = - 3x + 4 ( divide all terms by - 2 )
y = x - 2 ← not equivalent
B
2x - 3y = 12 ( subtract 2x from both sides )
- 3y = - 2x + 12 ( divide all terms by - 2 )
y = x - 4 ← equivalent
C
- 4(2x - 3y ) = - 48 ( divide both sides by - 4 )
2x - 3y = 12 ← same as B ⇒ equivalent
D
2(x + 6) = 3y
3y = 2x + 12 ( divide all terms by 3 )
y = x + 4 ← not equivalent
E
2x - 3y = 4 ( subtract 2x from both sides )
- 3y = - 2x + 4 ( divide all terms by - 3 )
y = x -
← not equivalent
To find the vertex of our parabola, we are going to use the vertex formula: For a quadratic of the form 
it vertex 
is given by 
, 
.
We can infet from our parabola that
and 
. So lets replace those values in our formula:
The vertex of our parabola is 
Now to find our second point, we are going to evaluate our parabola at
Our second point is
We can conclude that we can graph the parabola
using its vertex and the point as follows:
We can infet from our parabola that
The vertex
Now to find our second point, we are going to evaluate our parabola at
Our second point is
We can conclude that we can graph the parabola