are these 2 equations for lines perpendicular, parrel, or neither?? i dont understand how to solve line equations very well.:
y= -2/3 x +1
2x - 3y= -3
get both equations into slope-intercept form (solve for y)
2x - 3y= -3 ... -3y = -2x - 3 ... y = 2/3 x + 1
parallel lines have the same slope
perpendicular lines have slopes that are negative-reciprocals
these two appear to be neither
that makes sense, actually, THANKS!
Eq1: slope = -2/3.
Eq2: slope = -A/B = -2/-3 = 2/3.
Answer: neither.
To determine whether two lines are perpendicular, parallel, or neither, we need to compare their slopes.
The slope-intercept form of a line is y = mx + b, where m represents the slope of the line. In your first equation, y = -2/3x + 1, the slope is -2/3.
To find the slope of your second equation, we need to rearrange it into the slope-intercept form. Start by isolating y:
2x - 3y = -3
-3y = -2x - 3
y = (2/3)x + 1
Now we can see that the slope of the second equation is 2/3.
If the slopes of two lines are the same, they are parallel. If the slopes are negative reciprocals of each other (i.e., multiplying one slope by -1 gives the other slope), the lines are perpendicular. In this case, the slopes are -2/3 and 2/3, which are negative reciprocals of each other.
Therefore, the two lines represented by the given equations are perpendicular.