is this line that passes through (-6,2) and (4,8)parallel to the line -3x+5y=15?
HELP ME OUT PLEASE SOLVE IT..............
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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!
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.