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

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)