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.

MD
Answered by M D. Maths tutor

6811 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

What is 3!/5! written in standard form?


There are only red , blue and purple counters in a bag. The ratio of the number of red counters to the number of blue counters is 3 : 17. If a counter is taken randomly the probability that it is purple is 0.2 Work out the probability for it to be red.


How can i solve the following simultaneous equations? 5x + y = 4 and 3x + 2y = 5?


factorise x^2+5x+6=0 and find x


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences