Question

Given the following questions determine if the lines are parallel perpendicular or neither

Answer 1

Given the equations:

`\begin{gathered} (4y+11x)/(4)=x+2 \\ \\ 3x-7y=7x+10 \end{gathered}`

Let's determine if the lines are parallel or perpendicular.

Rewrite both equations in slope-intercept form:

y = mx + b

Where m is the slope.

Rewrite each equation for y.

• Equation 1:

`\begin{gathered} (4y+11x)/(4)=x+2 \\ \\ 4y+11x=4(x+2) \\ \\ \text{ Apply distributive property:} \\ 4y+11x=4x+8 \\ \\ \text{ Subtract 11x from both sides:} \\ 4y+11x-11x=4x-11x+8 \\ 4y=-7x+8 \\ \text{ Divide all terms by 4:} \\ (4y)/(4)=-(7)/(4)x+(8)/(4) \\ \\ y=-(7)/(4)x+2 \end{gathered}`

• Equation 2:

`\begin{gathered} 3x-7y=7x+10 \\ \\ Subtract\text{ 3x from both sides:} \\ 3x-3x-7y=7x-3x+10 \\ \\ -7y=4x+10 \\ \\ \text{ Divide all terms by -7:} \\ -(7y)/(-7)=(4)/(-7)x+(10)/(-7) \\ \\ y=-(4)/(7)x-(10)/(7) \end{gathered}`

Therefore, we have both equations in slope-intercept form:

`\begin{gathered} y=-(7)/(4)x+2 \\ \\ y=-(4)/(7)x-(10)/(7) \end{gathered}`

• The slope of equation 1 is: -7/4

,

• The slope of equation 2 is: -4/7

Parallel lines have equal slopes.

Perpendicular lines have slopes that are the negative reciprocal of each other.

Since both slopes are neither equal nor negative reciprocals, then both lines are neither parallel nor perpendicular.

• ANSWER:

Neither