SOLUTION: Given below are descriptions of two lines. Line 1: Goes through (-11,-9) and (2,4). Line 2: Goes through (-4,0) and (-15,-11). The slope of Line 1 The slope of Line 2

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Given below are descriptions of two lines. Line 1: Goes through (-11,-9) and (2,4). Line 2: Goes through (-4,0) and (-15,-11). The slope of Line 1 The slope of Line 2       Log On


   

Question 1205656: Given below are descriptions of two lines.
Line 1: Goes through (-11,-9) and (2,4).
Line 2: Goes through (-4,0) and (-15,-11).
The slope of Line 1
The slope of Line 2
Finally, which of the following is true?
Line 1 is parallel to Line 2.
Line 1 is perpendicular to Line 2.
Line 1 is neither parallel nor perpendicular to Line 2.
Found 3 solutions by josgarithmetic, MathLover1, math_tutor2020:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Simply apply formula for slope through two points.

For "Finally" part, lines are perpendicular is slopes are negative reciprocal of each other. If slope are equal but pair makes DIFFERENT lines in the plane then the lines parallel. You decide about if the last part is true or not.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Line 1: Goes through (-11,-9) and (2,4).
Line 2: Goes through (-4,0) and (-15,-11).
The slope of Line 1
m=%284-%28-9%29%29%2F%282-%28-11%29%29=%284%2B9%29%2F%282%2B11%29=13%2F13=1
The slope of Line 2
m=%28-11-0%29%2F%28-15-%28-4%29%29=-11%2F%28-15%2B4%29=-11%2F-11=1

Finally, which of the following is true?
Line 1 is parallel to Line 2.=>true
Line 1 is perpendicular to Line 2.
Line 1 is neither parallel nor perpendicular to Line 2.

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Let's compute the slope of line 1.




m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29

m+=+%284+-+%28-9%29%29%2F%282+-+%28-11%29%29

m+=+%284+%2B+9%29%2F%282+%2B+11%29

m+=+%2813%29%2F%2813%29

m+=+1
Line 1 has a slope of 1.

Now apply point-slope form to find the equation of line 1.
y+-+y%5B1%5D+=+m%28x+-+x%5B1%5D%29

y+-+%28-9%29+=+1%28x+-+%28-11%29%29

y+%2B9+=+1%28x+%2B11%29

y+%2B9+=+x+%2B11

y+=+x+%2B11-9

y+=+x+%2B2
The equation of line 1 is y = x+2

Repeat a similar process for line 2.
I'll skip steps but you should get y = x+4

Both equations have the same slope (m = 1), but different y intercepts.
Therefore the lines are parallel.
You can use a graphing tool like Desmos or GeoGebra to confirm.