I need toIs the following pair of lines parallel or perpendicular? Prove your answer.
2y – x = 2
y + 2x = 4
can you explain how to break this down ...
you need to get it into slope intercept form--y=mx+b
(m being the slope) to figure out whether they are parallel (having equal slopes) or perpendicular (slopes are negative reciprocals)
2y-x=2
2y=x+2
y=1/2x+1
slope=1/2
y+2x=4
y=-2x+4
slope=-2
-2 and 1/2 are negative reciprocals making these two line perpendicular
Thank you I did not see the answer. Thank you so much
To determine if two lines are parallel or perpendicular, we need to examine the slopes of the lines. If the slopes are the same, the lines are parallel. If the slopes are negative reciprocals of each other, the lines are perpendicular.
To find the slopes, we need to rewrite the equations in the slope-intercept form (y = mx + b), where "m" represents the slope.
Given equations:
2y - x = 2
y + 2x = 4
Let's solve the first equation for y:
2y - x = 2
2y = x + 2
y = (1/2)x + 1
The slope of the first line is 1/2.
Now, let's solve the second equation for y:
y + 2x = 4
y = -2x + 4
The slope of the second line is -2.
Since the slopes are not equal and not negative reciprocals, the lines are neither parallel nor perpendicular.