# Gradient Intercept Form of Equation of line (linear function)

Author:
Lew W. S.

## Equation of a straight line (function)

The graph of y = mx + c is shown below. i. Use the sliders m and c to change their values. ii. You can also use button "Trace line/graph of function" to trace the line. How do the lines behave as values of m, c are changed. iii. For question 3, you can enter a second linear equation into the input box (with beige background).

## 1. What is "c"

Observe how the line changes as you change the values of c from -4 to 4 What can you say about the line when c changes? Is there any significance between the value of c and the point where the line cuts the y axis? Can you explain this connection using algebra?

## 2. How "m" affects the graph

Observe how the line changes as you change the values of m from -3 to 3. What can you say about the line when m changes? Where is the point on the line which does not change its position as m changes? Can you explain this using algebra?

## 3. Form of equation

Set the graph with m = 3 and c = -2. Now type in a new equation 6x - 2y = 4 in the input box (beige) What do you observe about the new line created with the above equation? Is y = 3x - 2 the equivalent to 6x - 2y = 4 ? Explain algebraically.

## 4. Conclusion :

An equation of the form ax + by = c is can be rewritten as _________________ where ______________ = ________________ and ____________ = _____________ (for fraction three quarters (or 0.75) type as 3/4 ) Type out your answer, for each question, onto the space below.