tell whether the lines for each pair of equations are parallel, perpendicular, or neither. a=parallel, b=perpendicular, c= neither
A. y=6x+2 and 18x-3y=15
B. 2x - 5y=0 and y+3=5/2x
A. To find out if the lines are parallel, perpendicular, or neither, we need to compare the slopes of the lines.
The slope-intercept form of a line is y = mx + b, where m is the slope.
For y = 6x + 2, the slope is 6.
For 18x - 3y = 15, we need to put it in slope-intercept form.
18x - 3y = 15
-3y = -18x + 15
y = 6x - 5
Comparing the slopes, we see that both slopes are 6. Therefore, the lines are parallel.
The answer is a) parallel.
B. Again, we need to compare the slopes of the lines.
For 2x - 5y = 0, rearrange to find the slope-intercept form:
-5y = -2x
y = 2/5x
Comparing the slopes, we see that one is 2/5 (for y = 2/5x) and the other is 5/2. The product of the slopes, 2/5 and 5/2, is -1. This indicates that the lines are perpendicular.
The answer is b) perpendicular.