Determine whether the given pairs of lines are parallel, coincident, or intersecting.
L: x+y=10
M: 3x+3y+6
where does the equal sign go in the 2nd expression?
assuming your 2nd equation says:
3x + 3y = 6
divide each term by 3
x + y = 2
your first equation is x+y = 10
so they have the slope, but two different constants, thus
two parallel lines
To determine whether the given pairs of lines are parallel, coincident, or intersecting, we need to compare their slopes.
The equations of the lines are:
L: x + y = 10
M: 3x + 3y + 6 = 0
Step 1: Write the equations in slope-intercept form (y = mx + b).
L: y = -x + 10
M: 3y = -3x - 6
Divide both sides by 3.
y = -x - 2
Step 2: Compare the slopes.
The slope of line L is -1, and the slope of line M is -1.
Step 3: Determine if the slopes are equal.
Since the slopes of L and M are equal, the lines are parallel.
Therefore, the given pair of lines L and M are parallel.
To determine whether the given pairs of lines are parallel, coincident, or intersecting, we need to compare their slopes. The given lines are:
L: x + y = 10
M: 3x + 3y + 6
To find the slopes of the lines, we need to rewrite them in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
For line L, we rearrange the equation to isolate y:
y = -x + 10
Comparing this to slope-intercept form, we can see that the slope of line L is -1.
For line M, we rearrange the equation to isolate y:
3y = -3x - 6
y = (-3/3)x - 2
y = -x - 2
Comparing this to slope-intercept form, we can see that the slope of line M is -1 as well.
Since the slopes of both lines L and M are equal (-1), the lines are parallel to each other.