Write the equation of the line perpendicular to y=3/2x+1/2 that passes through the point (-2,9).

Answer 1

The equation of a line is where algebra and coordinate geometry come together. A Y-point equals an X-point multiplied by the slope or slant of the line plus the point on the Y-axis where the line crosses or intercepts. We write this as Y = mX + b. If we start with the b or 1/2 of the given equation and use the m or 3/2 to go up 3 and right 2 from the point 1/2 on the Y-axis, we get the point (2,3 and 1/2). By connecting the two points, we get our starting line. To write an equation of a line perpendicular to the starting line, we need to find a new m and a new b. Our new m has a sign that's the opposite of the old m and a fraction that's the old flipped. By substituting the point (-2,9) for X and Y in Y = mX + b, we can solve for the new b. So our answer is Y = (new m) X + new b.

Answer 2

The line perpendicular to the given line must have slope equal to -(2/3). Since we need the line to pass through the point (-2,9) we get the equation 9=-(2/3)(-2)+B which implies that B=23/3. Hence, the required equation is y=(-2/3)x+23/3.