Question

Determine if y=-⅓x+5 is parallel to 2x+6y=12

Answer 1

`\textsf{Two lines are parallel if their slopes are equal.}\\\textsf{We are given two lines,}\\\\\textsf{y=}\sf{-(1)/(3)x+5............(1)}\\\\\textsf{2x+6y = 12..........(2)}`

`\textsf{Comparing equation(1) with y = mx + c,}\\\textsf{We get slope of the line = }-(1)/(3)`

`\textsf{Slope of line (2) = }\sf{-(coefficient\ of\ x)/(coefficient\ of\ y)=(-2)/(6)=(-1)/(3)}`

`\textsf{The slopes of line(1) and line (2) are equal, hence, these lines are parallel to each}\\\textsf{other.}`