What is the relationship of the two lines with the equations -3y=x-6 and y=3x+1?
I am very confused.
Please explain how you got your answer!
change the first to
y = (-1/3)x + 2
notice the slopes are negative reciprocals.
Does that ring a bell ?
perpendicular! thank you so much!
To determine the relationship between the two lines with the equations -3y = x - 6 and y = 3x + 1, we can compare the slopes and y-intercepts of the equations.
Let's begin by rewriting both equations in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
For the equation -3y = x - 6:
1. Divide both sides by -3: y = -1/3x + 2
For the equation y = 3x + 1, you can see that the equation is already in slope-intercept form.
Now that both equations are in slope-intercept form, we can compare their slopes and y-intercepts.
Comparing the slopes:
The slope of the first equation is -1/3, and the slope of the second equation is 3. Since the slopes are different, the lines are not parallel.
Comparing the y-intercepts:
The y-intercept of the first equation is 2, and the y-intercept of the second equation is 1. Since the y-intercepts are also different, the lines do not have the same y-intercept.
Based on this information, we can conclude that the two lines are not parallel and have different y-intercepts. Therefore, the relationship between these two lines is that they intersect at a single point.
If you would like to verify this visually, you can graph both equations on the Cartesian plane and observe where they intersect.