The equation of the parallel line is y = [tex]\frac{-2}{3}[/tex] x + [tex]\frac{22}{3}[/tex] ⇒ 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 [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
∵ Line EF has E (-2 , 5) and F (1 , 3)
∴ [tex]x_{1}[/tex] = -2 and [tex]x_{2}[/tex] = 1
∴ [tex]y_{1}[/tex] = 5 and [tex]y_{2}[/tex] = 3
- Use the formula of m above to find the slope of line EF
∴ [tex]m_{EF}=\frac{3-5}{1--2}=\frac{-2}{3}[/tex]
∵ The line is parallel to line EF
∴ Their slopes are equal
∴ The slope of the parallel line is [tex]\frac{-2}{3}[/tex]
- Substitute the slope of the line in the form of the equation
∴ y = [tex]\frac{-2}{3}[/tex] 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 = [tex]\frac{-2}{3}[/tex] (2) + b
∴ 6 = [tex]\frac{-4}{3}[/tex] + b
- Add [tex]\frac{4}{3}[/tex] to both sides
∴ [tex]\frac{22}{3}[/tex] = b
∴ y = [tex]\frac{-2}{3}[/tex] x + [tex]\frac{22}{3}[/tex]
The equation of the parallel line is y = [tex]\frac{-2}{3}[/tex] x + [tex]\frac{22}{3}[/tex]
Learn more:
You can learn more about the equations of the parallel lines in brainly.com/question/9527422
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