Find the equation of the line in the form of y=mx+c given that two points on the line are (3,1) and (6,10)

Firstly, we can solve this equation by drawing a graph. By drawing it accurately we can see that the line intercepts the y-axis at -8 making the c value = -8. Next to calculate the gradient, m, we can take any two points on the line, in this case I will take (0,-8) and (3,1). The gradient is the change in y divided by the change in x. 1-(-8)=9 which is the change in y and 3-0 is the change in x. 9/3=3 which is the m value. So the equation of the line is y=3x-8.We can also solve this algebraically. Similarly to find the gradient, we can take the two coordinates which have been given to us, (3,1) and (6,10) and find the difference in y divided by the difference in x. 10-1=9 which equals the change in y and 6-3=3 which equals the change in x. 9/3 is 3 so m=3. We can then use these values to find c. By substituting one of the coordinates into our y=mx+c equation, (3,1) in this case, we get 1=3(3)+c. This simplifies to 1=9+c so c=-8. This method can be used to solve any linear equation from two points.