Question

Given the information below, identify which equations are parallel and which are perpendicular. A. LaTeX: y=\frac{1}{2}x+5y = 1 2 x + 5 B. LaTeX: y-3=-2\left(x+7\right)y − 3 = − 2 ( x + 7 ) C. LaTeX: 2x+y=9

Answer 1

Perpendicular equations: 1 and 2, 1 and 3

Parallel equations: 2 and 3

Explanation:

The three equations are:

`y=(1)/(2)x+5` ...Equation 1

`y-3=-2(x+7)`

Expanding the bracket, we have,

`y-3=-2x-14\\\\y=-2x-14+3\\\\y = -2x-11`

`y=-2x-11` ...Equation 2

`2x+y=9\\\\y = 9-2x\\\\`

`y = -2x + 9` ...Equation 3

For two equations to be perpendicular, the product of their slopes must equals -1.

For two equations to be parallel, their slopes must be equal.

The equation of a straight line is:
`y=mx+c`

Where m = slope (or tangent) of the equation.

For equation 1, slope1 = 1/2

For equation 2, slope2 = -2

For equation 1, slope3 = -2

Slope1 * Slope 2 =
`(1)/(2)*-2=-1`

Therefore, equations 1 and 2 are perpendicular.

Slope 1 * Slope 3 =
`(1)/(2)*-2=-1`

Therefore, equations 1 and 2 are perpendicular.

Slope 2 = Slope 3 = -2

Therefore, equations 2 and 3 are parallel.