The point P has coordinates (3,4), Q has the 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

Firstly, let's have a look through the question to find the key words and write down any equations you might need. Perpendicular means the two lines cross and meet at a right angle, we also have an equation for the gradient of two perpendicular lines m1m2=-1 (where m is the gradient of the lines).Rearrange the equation into the format of y=mx+c, this gives y=-(3/2)x + (7/2). We can then put -(3/2) into m1m2=-1 - this gives 2/3. So the gradient of the line we're trying to find is 2/3. Now we can express our line as y=2/3x+ c. To find c input point P - c is 2. Now our equation is y=2/3x+2. If we put in point Q we're actually expressing the line b in terms of a - b=2/3a+2