Determine whether the graphs of y= 2x + 4 and x + 2y = 6 are parallel lines

Answer 1

Parallel Lines :

• If two nonvertical lines in the same plane have the same slope, then they are parallel.

• If two nonvertical lines in the same plane are parallel, then they have the same slope.

The equations of two lines are y = 2x + 4 and x + 2y = 6.

The equation 1 : y = 2x + 4 is already adjusted in slope - intercept form or y = mx + b and its slope m₁ = 2.

Write the equation 2 : x + 2y = 6 in slope intercept form or y = mx + b.

2y = - x + 6

y = - (1/2)x + 3

The slopes of two lines are m₁ = 2 and m₂ = - 1/2 and these are not same.

Therefore, the graphs of y = - 2/3x and 3x - 2y = 6 are do not parallel lines.

 

Answer 2

Parallel lines have same slope. So, find the slopes of the lines.

Slope-intercpt form line equation is y = mx + b, where m is slope and b is y-intercept.

First line y = 2x + 4 is already in slope-intercept form.

So, slope of the line is m = 2

Second line equation is x + 2y = 6

Subtract x from each side

2y = -x + 6

Divide each side by 2

y = -1/2 x+ 3

Slope of the line = -1/2

Since slopes are not equal they are not parallel.