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

Author:
Lew W. S.
This is a self mastery practice activity. Score yourself at least 10 marks to master this. Some refreshers: (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. Go ahead and do the practice below (Observe the answer steps for each attempt)