SOLUTION: 6. Are the following pairs of line parallel, perpendicular, or neither. L1 with equation x + 2y = 4 L2 with equation 2x + 4y =5

Question 121230: 6. Are the following pairs of line parallel, perpendicular, or neither.

L1 with equation x + 2y = 4
L2 with equation 2x + 4y =5

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First convert the standard equation into slope intercept form

Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)

Convert from standard form (Ax+By = C) to slope-intercept form (y = mx+b)

Start with the given equation

Subtract 1x from both sides

Simplify

Divide both sides by 2 to isolate y

Break up the fraction on the right hand side

Reduce and simplify

The original equation (standard form) is equivalent to (slope-intercept form)

The equation is in the form where is the slope and is the y intercept.

Now convert the standard equation into slope intercept form

Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)

Convert from standard form (Ax+By = C) to slope-intercept form (y = mx+b)

Start with the given equation

Subtract 2x from both sides

Simplify

Divide both sides by 4 to isolate y

Break up the fraction on the right hand side

Reduce and simplify

The original equation (standard form) is equivalent to (slope-intercept form)

The equation is in the form where is the slope and is the y intercept.

Since the two slopes are both , this means that the two slopes are equal. This also means that the two lines are parallel

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Answer:

So the lines and are parallel.
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