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)