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
in a), is the coefficent of x the same in each equation?
in b), put the first equation into the form y= mx+b. Then, is m=5 as in the second equation?
y=3x+2, y=1/3x+4
To determine whether the graphs of the two equations are parallel lines, we need to compare their slopes. Parallel lines have the same slope.
a. For the equations, y = 3x + 2 and y = 1/3x + 4, the slopes are 3 and 1/3, respectively. Since the slopes are different, the graphs of the two equations are not parallel lines.
To calculate the slope of each equation, the general form of a linear equation is y = mx + b, where m is the slope. In equation a, the coefficient of x is 3, so the slope is 3. In equation b, the coefficient of x is 1/3, so the slope is 1/3.
b. For the equations, 3y = 15x + 4 and y = 5x + 1, we can rearrange them in the form y = mx + b. Dividing the first equation by 3 gives us y = 5x + 4/3. Now we can see that the equation is similar to y = 5x + 1, which means the slopes of both equations are 5. Since the slopes are the same, the graphs of the two equations are parallel lines.
To calculate the slope of the first equation, we rearranged it to y = 5x + 4/3, where the coefficient of x is 5, so the slope is 5. For the second equation, y = 5x + 1, the coefficient of x is also 5, so the slope is 5. Since the slopes of both equations are the same, the graphs are parallel lines.