What is the relationshiip between the lines of these two equations?:
2x+3y=12
y=-2/3x-20
They are parallel, right?
A good way to be sure is to put the lines into the familiear y=mx+b form.
The second equation is already there. If the value of m is the same, the lines are parallel.
since 2x+3y=12 isnt in a famliiar form put it in standard form...... so y=-2/3x+4 and you can figure the rest out cuz i don't remember that was from like Unit 5 and im in unit 12
To determine the relationship between the lines represented by these two equations, we need to compare their slopes. The slope-intercept form of a linear equation is given by y = mx + b, where m represents the slope and b represents the y-intercept.
Let's first identify the slopes of the two lines. In the first equation, 2x + 3y = 12, we can rearrange it into slope-intercept form by isolating y:
2x + 3y = 12
3y = -2x + 12
y = (-2/3)x + 4/3
For the second equation, y = -2/3x - 20, since it's already in slope-intercept form, we can directly observe its slope, which is -2/3.
By comparing the slopes of the two equations, we can determine their relationship. If the slopes are equal, it means the lines are parallel. If the slopes are different, the lines are not parallel.
In this case, the slope of the first equation is -2/3, and the slope of the second equation is also -2/3. Since the slopes are the same, we can conclude that the lines represented by these two equations are indeed parallel.