The point P has coordinates (3, 4) The point Q has coordinates (a, b) A line perpendicular to PQ is given by the equation 3x + 2y = 7 Find an expression for b in terms of a.

The first step should be to rearrange the equation of the perpendicular line to PQ, in order to find the gradient, which works out to -3/2x. This can be done using the equation y=mx+c, where m is the gradient. Then we can use another rule, the fact that if the gradients of two lines are multiplied together, and the answer is -1, that shows that the two lines are in fact perpendicular. Using that concept we can work out the gradient of the line PQ, by calculating -3/2 x m = -1. Here the x represents a multiplication symbol, and m represents the gradient of the line PQ. This works out to be 2/3. The next step is to put the values of P, a coordinate we already know which lies on the line PQ, into the equation of a straight line, y=mx+c, with the gradient we previously worked out, in order to find the "c" in that equation, the y-axis intercept. Hence we will be working out 4=(3*2/3) + c. From this we can work out that c=2. Therefore we have the full equation, y=2/3x + 2. The final answer mark to gain would be to re-write the equation, in terms of b with respect to a, which would be, b=2/3a +2.

Answered by M D. Maths tutor

6170 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Factorise (x^2-100) and then solve for x.


Given that y is directly proportional to square root of x and that y = 20 when x = 49 find an expression to represent x and y.


If the probability of picking a red ball out of bag A is 2/5 and the probability of picking a red ball out of bag B is 3/7, what is the chance that you will pick exactly 2 red balls if you pick 2 balls from A and 1 ball from B? The balls are not replaced.


Solve the simultaneous equations: 3x + y = 15 and 4y + 3 = 9x


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo
Cookie Preferences