Point (-12 , 8) is on the line that passes through (0, 6) and is parallel to the given line ⇒ 1st
Step-by-step explanation:
Parallel lines have:
- Same slopes
- Different y-intercepts
The formula of the slope of a line which passes through points [tex](x_{1},y_{1})[/tex] and [tex](x_{1},y_{1})[/tex] is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
∵ The given line passes through points (-12 , -2) and (0 , -4)
∴ [tex]x_{1}[/tex] = -12 , [tex]x_{2}[/tex] = 0
∴ [tex]y_{1}[/tex] = -2 , [tex]y_{2}[/tex] = -4
- Use the formula of the slope above to find the slope of the given line
∵ [tex]m=\frac{-4-(-2)}{0-(-12)}=\frac{-4+2}{12}=\frac{-2}{12}=\frac{-1}{6}[/tex]
∴ The slope of the given line is [tex]\frac{-1}{6}[/tex]
∵ The two lines are parallel
∴ Their slopes are equal
∴ The slope of the parallel line = [tex]\frac{-1}{6}[/tex]
∵ The parallel line passes through point (0 , 6)
- The form of the linear equation is y = mx + b, where m is the slope
and b is the y-intercept (y when x = 0)
∵ m = [tex]\frac{-1}{6}[/tex] and b = 6
∴ The equation of the parallel line is y = [tex]\frac{-1}{6}[/tex] x + 6
Let us check which point is on the line by substitute the x in the equation by the x-coordinate of each point to find y, if y is equal the y-coordinate of the point, then the point is on the line
Point (-12 , 8)
∵ x = -12 and y = 8
∵ y = [tex]\frac{-1}{6}[/tex] (-12) + 6
∴ y = 2 + 6 = 8
- The value of y is equal the y-coordinate of the point
∴ Point (-12 , 8) is on the line
Point (-12 , 8) is on the line that passes through (0, 6) and is parallel to the given line
Learn more:
You can learn more about the equations of parallel lines in brainly.com/question/9527422
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