Mathematics
Mathematics
Problem
Answer the following questions about two lines. a. (i) Convert the equations and to slope–intercept form and hence find the slope of each line. b. (ii) Determine whether the two lines are parallel, perpendicular, or neither. Give a brief reason for your conclusion. c. (iii) Find the equation of the line that passes through the point and is parallel to both of the above lines. d. (iv) Find the equation of the line that passes through and is perpendicular to each of the above lines.Intuitive explanation
When two lines meet in a plane, their relationship is determined by their slopes and positions. The key insight is that parallel lines have equal slopes, while perpendicular lines have slopes whose product equals . By comparing slopes and checking whether lines share a point, you can classify their relationship and solve for unknowns like missing coefficients or intersection coordinates.
Intuitive explanation
When two lines meet in a plane, their relationship is determined by their slopes and positions. The key insight is that parallel lines have equal slopes, while perpendicular lines have slopes whose product equals . By comparing slopes and checking whether lines share a point, you can classify their relationship and solve for unknowns like missing coefficients or intersection coordinates.