HELP ME OUT PLEASE SOLVE IT..............

Question

is this line that passes through (-6,2) and (4,8)parallel to the line -3x+5y=15?

Answer 1

This is easily solved if you know vectors. Vector from (-6,2) to (4,8) has coordinates (4-(-6), 8-2)=(10,6). In the line equation ax+by=c coefficients a and b are coordinates of a vector perpendicular to the line. In your case it is vector (-3,5). If the vector from (-6,2) to (4,8) is perpendicular to the vector, perpendicular to the line -3x+5y=15, then it means it is parallel to the line itself, and so is the line passing through those points. Form a scalar product of two vectors:

 

(10,6)•(-3,5)=10*(-3)+6*5=-30+30=0. Since scalar product of two vectors is zero, they are indeed perpendicular to each other and the line through points is parallel to the line -3x+5y=15. Answer: yes.

 

Alternatively, write your line equation in the slope-intercept form:

 

-3x+5y=15 ⇔ y=3/5x+3; Slope is 3/5. Find the slope of the line passing through the points (-6,2) and (4,8).

 

slope=(difference in y coordinates)/(difference in x coordinates)=(8-2)/(4-(-6))=6/10=3/5. Lines have equal slopes, thus it means they are parallel. Answer: yes.

Answer 2

parallel lines have equal slopes. Find the slope of each and compare.

 

to find the slope between 2 points:  use slope formula (y₁- y₂)  / (x₁ - x₂) = (2 - 8) / (-6 - 4) = -6 / -10 = 3/5

 

to find the slope of a line that is already an equation, change the equation to slope intercept form y = mx +b

 

Solve for y:  -3x + 5y = 15      first add 3x to BOTH SIDES of the equals sign.  It will cancel on the left and then say 15 + 3x on the right.  so the equation is now written as 5y = 15 + 3x.  I'm going to switch the -3x and 15 around because usually the form has the "x" term right after the equals sign and the constant number after that.  so 5y = 3x +15. 

 

Now divide everything by 5, everything.   The 5's cancel on the left and we do a little math on the right to clean up.

 

y = 3/5 x +3.  When in slope intercept form, the "m" is the slope and it is always the number in front of the x(called the coefficient).  Our m = 3/5

 

does 3/5 = 3/5?  Yes so the lines are parallel.

 

 **Thanks Krill! I didn't see my mistake till you pointed it out!  I fixed it!