How can I find the equation of a straight line on a graph?

One good way is to use the formula y - y₁ = m(x - x₁)where (x₁,y₁) is a point on the line and m is the gradient of the line. This is derived from the definition of the gradient m=(y₂-y₁)/(x₂-x₁)What is the equation of the line perpendicular to y = 2x +10 that passes through the point (1, 12)? Give your answer in the form ax + by + c = 0 where a, b, and c are integers. First draw out the problem. We need a point on the line we are trying to find (the perpendicular) and this is given in the question as (1,12).Therefore x₁=1 and y₁=12.Next we have to find the gradient of the perpendicular line. The original gradient is 2. The perpendicular gradient is the negative reciprocal so m = -1/2.Now we have all the values we need to substitute back into the original formula, y - y₁ = m(x - x₁).This gives: y - 12 = -1/2 (x - 1).
Always finish of your answer by rereading the question and making sure you give you answer in the correct form. To re-arrange to ax + by + c = 0 first get rid of the brackets by multiplying by -2:-2(y-12) = x - 1-2y +24 = x - 1-2y - x + 24 = -1-2y - x + 25 = 0This is a perfectly acceptable answer but if you will be using it for further questions you may find it easier to multiply both sides by -1 giving2y + x - 25 =0
If you have time you should check your answer by substituting the point that is on the line, which should satisfy the equation.2(12) + 1 - 25 =24 + 1 - 25 +25 -25 = 0 as required