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,

$Slope\text{ = }\frac{-a}{b}$

The slope of the above line is calculated as,

$Slope(1)\text{ = }\frac{-1}{3}$

Equation of the second line is given as,

$2x+6y=24$

The equation of the second line is calculated as,

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

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.