Prove that the lines 2y=3-x and y-2x=7 are pependicular.

We can find out whether lines are perpendicular by comparing their gradients. Each gradient should be the negative reciprocal of the other - for example, 3/2 and -2/3, or 4 and -1/4. (Writing the number as a fraction, then flipping the top and bottom of the fraction and reversing the +/- sign should give you the negative reciprocal.)

To work out the gradient of a straight line, we must rearrange the equation into the form y=mx+c, where m is the gradient and c represents a constant which is the y-intercept (the point at which the line crosses the y-axis).

Rearranging the first equation:

2y = 3 - x  -->   2y = -x + 3  -->  y= -1/2x + 3/2      The gradient, m, is -1/2

Rearranging the second:

y - 2x = 7  -->  y = 2x + 7     The gradient, m, is 2

Since 2 and -1/2 are negative reciprocals, the two lines must be perpendicular.