Find the gradient of the line 4x+9y=10.
There are two approaches to this problem.
Firstly, you could rearrange the equation so that you have the general equation of a line, y=mx+c, where m is the gradient that you are looking for! When we rearrange the equation, we get y=-4/9x+10/9 so the gradient is -4/9.
Also, we can use implicit differentiation to get the solution. We do this by differentiating both sides of the equation with respect to x. This gives us 4+9dy/dx=0. This can be rearranged to give dy/dx=-4/9. As we know the first derivative is the gradient - we can say the gradient of the line is -4/9.
DS
Related Maths A Level answers
All answers ▸simplify a^m x a^n
The line L1 has vector equation, L1 = ( 6, 1 ,-1 ) + λ ( 2, 1, 0). The line L2 passes through the points (2, 3, −1) and (4, −1, 1). i) find vector equation of L2 ii)show L2 and L1 are perpendicular.
You deposit 500 pounds at time t=0. At t=5 years, you have 800 pounds. The amount of money you have in the bank can be modeled as V(t)=A*(1+r)^t, where r is the interest rate. Find A and the interest rate r. After how many years will you have 1200 pounds.
What is the tangent line to the curve y = x^3+4x+5 at the point where x = 2?