decide whether the graphs of the two equations are parallel lines:
1. 2x+3y=5
9y+6x-1=0
answer: yes
2. 15+3x-10y=0
30x+24=10y
answer: yes
please check if this is right. thanks
1. correct.
2.
When the lines are given in standard form (Ax+By+C), they are ideal for checking parallelism and perpendicularity because if there is a vertical line, the y term will simply disappear, i.e. B=0, while in the slope-intercept form, the slope m will become infinity, which is not the case here.
For checking parallelism, try to multiply or divide to equalise one of the two coefficients, A, or B, and compare the other one. C will be different for parallel lines.
15+3x-10y=0....(1)
30x+24=10y ....(2)
becomes
3x-10y+15 = 0, and
30x-10y+24 = 0
We see that B is equal while A is different, we conclude that the two lines are not parallel.
thank you! :)
You're welcome!
To determine if the graphs of two equations are parallel lines, we need to compare their slopes. If the slopes are equal, then the lines are parallel.
For the first set of equations:
1. 2x + 3y = 5
2. 9y + 6x - 1 = 0
To find the slope of the first equation, we need to rearrange it into slope-intercept form (y = mx + b), where m is the slope:
2x + 3y = 5
3y = -2x + 5
y = (-2/3)x + 5/3
Comparing this to the second equation, we can see that the coefficient of x is also -2/3. Therefore, the two lines have the same slope and are parallel.
For the second set of equations:
1. 15 + 3x - 10y = 0
2. 30x + 24 = 10y
Rearranging the first equation:
10y = 3x + 15
y = (3/10)x + 3/2
Comparing this to the second equation, we see that the coefficient of x is 3/10, which is the same as the slope of the first equation. Thus, the two lines have equal slopes and are parallel.
So, your answers are correct. Both sets of equations represent parallel lines.