Question

Which description best compares thegraphs given by the equations:x + 3y = 152x + 6y = 24O parallelO perpendicularintersecting but not perpendicularO None of the above.

Answer 1

The equation of the first line is given as,

`x+3y=15`

The slope of line ax+by+c=0 is given as,

`Slope\text{ = }(-a)/(b)`

The slope of the above line is calculated as,

`Slope(1)\text{ = }(-1)/(3)`

Equation of the second line is given as,

`2x+6y=24`

The equation of the second line is calculated as,

`\begin{gathered} Slope(2)\text{ = }(-2)/(6) \\ Slope(2)\text{ = }(-1)/(3)_\text{ \_\_\_\_\_\_\_\lparen2\rparen} \end{gathered}`

From equations (1) and (2),

The slope of line 1 = Slope of line 2

As the slope of the lines is equal therefore the lines are parallel to each other.