State if the lines are Parallel, Perpendicular, or Oblique. 8) 6x ─ 12y = 24 9) 4x + y = 5 10) ─2x + 7y = 14. 4x + 2y = 8 3x +12y = ─6 4x = 14y 11) Write the equation of a vertical line through (-3, 0). 12) Write the equation of a horizontal line through (0. 8). Solve the systems of equations.
Line and surface integrals: Solutions. Example 5.1 Find the work done by the force F(x, y) = x2i − xyj in moving a particle along the curve which runs from Example 5.7 Find the area of the ellipse cut on the plane 2x + 3y + 6z = 60 by the circular cylinder x2 = y2 = 2x. Solution The surface S lies in the plane...
Purplemath. There is one other consideration for straight-line equations: finding parallel and perpendicular lines.Here is a common format for exercises on this topic: Given the line 2x – 3y = 9 and the point (4, –1), find lines, in slope-intercept form, through the given point such that the two lines are, respectively,:
(The slope-intercept form of the equation of a line states that y = mx + b. To find the slope-intercept form of the equation 6x − 2y − 4 = 0, you must isolate y on the left side of the equation, as follows: 6x−2y−4=0 −2y−4=−6x −2y=−6x+4 y=3x−2