Question

Find the equation of the line through point (2,−4) and parallel to −6x+2y=4

Answer 1

`\quad \huge \quad \quad \boxed{ \tt \:Answer }`

`\qquad \tt \rightarrow \: equation \: : \:y = 3x - 10`

____________________________________

`\large \tt Solution \: :`

Slope of parallel lines are equal.

`\texttt{Step 1 - Find slope of line -6x + 2y = 4}`

`\qquad \tt \rightarrow \: - 6x + 2y = 4`

`\qquad \tt \rightarrow \: 2( - 3 x+ y) = 2(2)`

`\qquad \tt \rightarrow \: - 3x + y = 2`

`\qquad \tt \rightarrow \: y = 3x + 2`

comparison with y = mx + c, m = slope = 3

`\textsf{Step 2 - Use slope and points to find equation}`

`\qquad \tt \rightarrow \: y - ( - 4) = 3(x - 2)`

`\qquad \tt \rightarrow \: y + 4 = 3x - 6`

`\qquad \tt \rightarrow \: y = 3x - 6 - 4`

`\qquad \tt \rightarrow \: y = 3x - 10`

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer 2

-------------------------------------------------------------------------------------------------------------

Answer:
`\textsf{y = 3x - 10}`

-------------------------------------------------------------------------------------------------------------

Given:
`\textsf{Goes through (2, -4) and parallel to -6x + 2y = 4}`

Find:
`\textsf{The equation that follows the criteria provided}`

Solution: First we need to solve for y in the equation that was provided so we can get the slope. Then we plug in the values into the point-slope formula and then solve for y to get our final equation.

Add 6x to both sides

• 
  `\textsf{-6x + 6x + 2y = 4 + 6x}`

• 
  `\textsf{2y = 4 + 6x}`

Divide both sides by 2

• 
  `\textsf{2y/2 = (4 + 6x)/2}`

• 
  `\textsf{y = (4 + 6x)/2}`

• 
  `\textsf{y = (4/2) + (6x/2)}`

• 
  `\textsf{y = 2 + 3x}`

Plug in the values

• 
  `\textsf{y - y}_1\textsf{ = m(x - x}_1\textsf{)}`

• 
  `\textsf{y - (-4) = 3(x - 2)}`

Distribute and simplify

• 
  `\textsf{y + 4 = (3 * x) + (3 * -2)}`

• 
  `\textsf{y + 4 = 3x - 6}`

Subtract 4 from both sides

• 
  `\textsf{y + 4 - 4 = 3x - 6 - 4}`

• 
  `\textsf{y = 3x - 6 - 4}`

• 
  `\textsf{y = 3x - 10}`

Therefore, the equation that follows the information that was provided in the problem statement is y = 3x - 10.