decide whether the pair of lines are parallel, perpendicular or neither?
2x + 3y =6
2x + 3y = 4
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To determine whether the pair of lines are parallel, perpendicular, or neither, we can examine the slopes of the two lines.
The given equations are:
1) 2x + 3y = 6
2) 2x + 3y = 4
To identify the slope of a line, we need to express each equation in slope-intercept form, y = mx + b, where m represents the slope.
For equation 1:
2x + 3y = 6
Rearranging the equation to slope-intercept form:
3y = -2x + 6
y = (-2/3)x + 2/3
The slope of equation 1 is (-2/3).
For equation 2:
2x + 3y = 4
Rearranging the equation to slope-intercept form:
3y = -2x + 4
y = (-2/3)x + 4/3
The slope of equation 2 is also (-2/3).
Since both lines have the same slope, (-2/3) in this case, the lines are parallel to each other.
Arrange the equations into the form
y=mx+c and find m for both.
if m are equal then the lines are parallel (same gradient)
if they are m and -m then they are perpendicular
otherwise neither.