# Explore gradient and y intercept of y = mx + c, ax + by = c, ax + by + c = 0

**This resource is for students to quickly explore equations of straight lines and how to find the gradient and y intercept.**(1)

**y = mx + c**is the function (or

**equation**of a straight line graph)

**in**

**gradient-intercept form**

**m is the gradient**, and

**c is the y intercept**.

**Graphical meaning of m and c**shown in https://www.geogebra.org/m/ssesmgqb (2) Linear equations in the form

**ax + by + c = 0**,

**ax + by = c**or

**by = ax + c**(where a, b and c are real numbers) can be reduced to their

**equivalent equations**in the gradient intercept form, ie y = mx + c. (

**additional self directed automated practices**at https://www.geogebra.org/m/fsgt7mp3 eg 4x + 2y - 6 = 0 ( of the form ax + by + c = 0) 2y = -4x + 6 (after subtracting 4x and adding 6 to both sides of the equation y = -2x + 3 (after dividing both sides of the equation by 2) which is of the form y = mx + c. (where m is the gradient and c is the y intercept) y = -2x + 3 is the equivalent equation of 4x + 2y - 6 = 0 using the balance principle of applying equal operations on both sides of an equation. Hence for the graph represented by the linear equation 4x + 2y = 6 = 0, the gradient of the graph is -2, and the y intercept is 3. Using the balance principle x - 2y = 4 is equivalent to y = 0.5 x + 2 Hence, the gradient is 0.5 and the y intercept is 2.

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