Question

PLEASE HELP!!

Answer 1

Answer:

3rd Choice

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Answer 2

The equation of the parallel line is y = $\frac{-2}{3}$  x + $\frac{22}{3}$ ⇒ 3rd answer

Step-by-step explanation:

Parallel lines has:

• Same slopes
• Different y-intercepts

The slope-intercept form of the equation of a line is y = mx + b, where

• m is the slope of the line and b is the y-intercept
• The formula of m is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

∵ Line EF has E (-2 , 5) and F (1 , 3)

∴ $x_{1}$ = -2 and $x_{2}$ = 1

∴ $y_{1}$ = 5 and $y_{2}$ = 3

- Use the formula of m above to find the slope of line EF

∴ $m_{EF}=\frac{3-5}{1--2}=\frac{-2}{3}$

∵ The line is parallel to line EF

∴ Their slopes are equal

∴ The slope of the parallel line is $\frac{-2}{3}$

- Substitute the slope of the line in the form of the equation

∴ y = $\frac{-2}{3}$ x + b

- To find b substitute x and y in the equation by the coordinates

   of a point on the line

∵ The parallel line passes through point (2 , 6)

∴ x = 2 and y = 6

∴ 6 = $\frac{-2}{3}$ (2) + b

∴ 6 = $\frac{-4}{3}$ + b

- Add $\frac{4}{3}$ to both sides

∴ $\frac{22}{3}$ = b

∴ y = $\frac{-2}{3}$  x + $\frac{22}{3}$

The equation of the parallel line is y = $\frac{-2}{3}$  x + $\frac{22}{3}$

Learn more:

You can learn more about the equations of the parallel lines in brainly.com/question/9527422

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