decide whether the graphs of the two equations are parallel lines.
a. y=3x+2, y=1/3x+4
b. 3y=15x+4, y=5x+1
do the lines in a) have the same slope?
do the lines in b) have the same slope?
I suppose..
You suppose wrong.
Put the sets of line in y=mx + b
and then compare the slope m. Parallel lines have the same slope.
To determine whether the graphs of two equations are parallel lines, we need to determine if their slopes (coefficients of x) are equal.
a. Let's compare the slopes of the two equations:
The first equation is y = 3x + 2.
The second equation is y = (1/3)x + 4.
Comparing the coefficients of x, we see that the slope of the first equation is 3, whereas the slope of the second equation is 1/3. Since the slopes are not equal, the graphs of these equations are not parallel lines.
b. Let's compare the slopes of the two equations:
The first equation is 3y = 15x + 4.
The second equation is y = 5x + 1.
To compare the slopes, we need to rewrite the first equation in the form y = mx + b, where m is the slope.
Dividing both sides of the first equation by 3, we get: y = 5x + 4/3.
Comparing the coefficients of x, we see that the slope of the first equation is 5, whereas the slope of the second equation is 5 as well. Since the slopes are equal, the graphs of these equations are parallel lines.
Therefore, for equation a, the graphs are not parallel lines, and for equation b, the graphs are parallel lines.