SOLUTION: Are the graphs of the lines in the pair parallel? Explain. y = 3x + 10 12x – 3y = –36

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Are the graphs of the lines in the pair parallel? Explain. y = 3x + 10 12x – 3y = –36      Log On


   

Question 945144: Are the graphs of the lines in the pair parallel? Explain.


y = 3x + 10

12x – 3y = –36
Found 2 solutions by MathLover1, macston:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
to determine if the graphs of the lines in the pair are parallel or not, all we need is to find slopes and if both slopes are equal, lines are parallel

y+=+highlight%283%29x+%2B+10...this line is already in slope-intercept form and we see that slope is 3

12x+-3y+=-36..this line need to be written in slope-intercept form first
12x+%2B36+=3y
12x%2F3+%2B36%2F3+=3y%2F3
y=highlight%284%29x+%2B12+ ...as you can see, the slope of this line is 4
since these lines have different slopes, we know they are NOT parallel; they intersect in one point
see it on a graph:
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+4x+%2B12%2C+3x+%2B+10%29+


Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
Lines with equal slopes are parallel, so put the equations in slope intercept form (y=mx+b, m is the slope)
y=3x+10 This equation is in correct form, and has a slope=3
12x – 3y = –36 Add 3y to each side
12x=3y-36 Add 36 to each side
12x+36=3y Divide each side by 3
4x+12=y Reverse sides of equation for clarity
y=4x+12 This equation has slope=4, which is not parallel to a line with slope=3
ANSWER No, the lines are not parallel.
+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+3x%2B10%2C+4x%2B12%29+
---OR---
If the lines have a common solution, they intersect and therefore are not parallel
Solve each equation for y and set the two equal (we've solved for y above)
y=3x+10
y=4x+12
3x+10=4x+12 Subtract 3x from each side
10=x+12 Subtract 12 from each side
-2=x
y=3(-2)+10
y=4
(-2,4) is a solution to this equation
12x-3y=-36
12(-2)-3(4)=-36
-24-12=-36
-36=-36
(-2.4) is also a solution to this equations, so the lines intersect,thus they are NOT parallel