Question

Put the equation y -7 =6(x+3) in standard form.

If the standard form, A= -6, what are the values of B and C.
Please show work

Answer 1

• B = 1
• C = 25

Explanation:

`\boxed{\begin{minipage}{5.5 cm}\underline{Standard form of a linear equation}\\\\$Ax+By=C$\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are constants. \\ \phantom{ww}$\bullet$ $A$ must be positive.\\\end{minipage}}`

The standard form of a linear equation Ax + By = C has the x and y terms on the left side and the constant on the right side. The coefficients of the variables must be integers.

• A is the coefficient of the term in x, which should be a positive integer.
• B is the coefficient of the term in y.
• C is the constant.

Given equation:

`y -7 =6(x+3)`

Expand the brackets:

`y-7=6x+18`

Switch sides:

`6x+18=y-7`

Subtract y from both sides:

`6x-y+18=-7`

Subtract 18 from both sides:

`6x-y=-25`

Therefore, the given equation in standard form is:

• 
  `6x-y=-25`

However, as your question states that A = -6, multiply both sides of the equation by negative 1 to make the coefficient of x negative:

• 
  `-6x+y=25`

Therefore,

• A = -6
• B = 1
• C = 25

Please note that this is not strictly in standard form, as A should be a positive integer.

Answer 2

A =-6, B = 1, and C =25

Explanation:

The equation y -7 = 6(x + 3) can be rearranged to the standard form y = Ax + B by isolating y on one side and collecting all the constant terms on the other side. To do this, we'll first expand the expression 6(x + 3) and then subtract 7 from both sides:

y - 7 = 6(x + 3)

y - 7 = 6x + 18

y = 6x + 25

So, the equation in standard form is:

y = 6x + 25

Now, if we are given that the standard form has A = -6, we can substitute this value into the equation:

y = -6x + B

since B is coefficient of y so

B=1

again

C is constant so C=25