Question

given the equation of the line 3x + 2y = 12, find (1) the gradient of the line. (2) the coordinates of the y-intercept

Answer 1

1.
Manipulate the equation into Slope-Intercept form: y = mx + b
m represents the slope (aka gradient)
3x + 2y = 12
Subtract 3x from both sides: 2y = -3x + 12
Divide both sides by 2: y = (-3/2)x + 6

The gradient is -3/2

2.
y-intercept is found when x-0
3x + 2y = 12
3(0) + 2y = 12
2y = 12
y = 6
The coordinate of the y-intercept is (6,0)