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.**

## Comments

_{2 }- y1)/(x_{2}-x_{1})