Equation of a Line[br]y=mx + c
1) Check the 'Show Equation' box to reveal the equation of the line.
(i) What is the coefficient of x for the equation of the line?
(ii) Calculate the gradient of the line y = x + 1.
(iii) What can you say about the coefficient of x and the gradient of the line for y = x + 1?
2) Adjust the slider for m such that m = 2.
(i) What is coefficient of x now?
(ii) Calculate the gradient of the line y = 2x + 1.
(iii) What can you say about the coefficient of x and the gradient of the line for y = 2x + 1?
3) Adjust the slider for m to various other values (including negative values) and calculate the gradients for the corresponding lines.[br][br]What can you conclude about the gradient of a line and the coefficient of x in the equation of the line?
4) Return the slider for m such that m = 1 and ensure that the slider for c = 1.
(i) State the constant value in the equation y = x + 1.
(ii) With reference to the graph, state the y-intercept of the line y = x + 1.
(iii) What can you say about the constant value in the equation and the y-intercept of the line?
5) Adjust the slider for c such that c = 2.
(i) State the constant value in the equation.
(ii) With reference to the graph, state the y-intercept of the line.
(iii) What can you say about the constant value in the equation and the y-intercept of the line?
6) 3) Adjust the slider for c to various other values (including negative values) and observe the y-intercept of the corresponding graphs.[br][br]What can you conclude about the y-intercept of a line and the constant in the equation of the line?