Question

I don’t know how to solve this I would love some help and explanations oh now to solve it please

Answer 1

2x + -3y = 19

Explanation:

In this question, they already gave you the equation of the line. But it is in point-slope form. We just need to rearrange the equation to look like:

Ax + By = C

A and B and C should be positive or negative whole numbers. So let's get rid of the fraction first.

y + 1 = 2/3 (x - 8)

You could use distributive property on the right side, but that is just going to make two terms have fractions. Instead, let's multiply both sides by 3 and get rid of the fraction.

3(y + 1) = 3• 2/3(x-8)

3(y + 1) = 2(x - 8)

Now use distributive property.

3y + 3 = 2x - 16

We need x and y on the left and plain numbers on the right.

3y + 3 = 2x - 16

Subtract 3

3y = 2x - 19

Subtract 2x

3y - 2x = -19

Rearrange the x and y terms, put x in the lead.

-2x + 3y = -19

This is almost standard form. The A is supposed to be positive. So change the sign of ALL the numbers. A is 2, the B is -3 and the C is 19. Those are the numbers that go in the blanks on your question.

Answer 2

Given the point-slope equation

`y+1=(2)/(3)(x-8)`

Simplify as shown below

`\begin{gathered} y+1=(2)/(3)x-8\cdot(2)/(3)=(2)/(3)x-(16)/(3) \\ \Rightarrow-(2)/(3)x+y=-(16)/(3)-1=-(19)/(3) \\ \Rightarrow-(2)/(3)x+y=-(19)/(3) \end{gathered}`

The answer is -2x/3+y=-19/3. Write -2/3 in the first gap, 1 in the second gap, and -19/3 in the third one.

How to multiply fractions

`\begin{gathered} (a)/(b)\cdot(c)/(d)=(a\cdot c)/(b\cdot d) \\ \Rightarrow8\cdot(2)/(3)=(8)/(1)\cdot(2)/(3)=(8\cdot2)/(1\cdot3)=(16)/(3) \end{gathered}`

How to add fractions,

`\begin{gathered} (a)/(b)+(c)/(d)=\frac{\text{ad+cd}}{bd} \\ \Rightarrow-(16)/(3)-1=-(16)/(3)-(3)/(3)=(-16\cdot3-3\cdot3)/(3\cdot3)=(-48-9)/(9)=-(57)/(9)=-(19)/(3) \end{gathered}`