Final answer:
The gradient of the line 6x + 2y + 9 = 0 is -3 after rearranging the equation to y = -3x - 4.5. The line crosses the y-axis at the point (0, -4.5) because that is the y-value when x is set to zero.
Step-by-step explanation:
The question involves finding the gradient of a line and where it crosses the y-axis given the equation 6x + 2y + 9 = 0.
Finding the Gradient
To find the gradient of the line, the equation needs to be in the form y = mx + b, where 'm' represents the gradient. Therefore, we first need to solve for y:
2y = -6x - 9
y = -3x - 4.5
From the rearranged equation y = -3x - 4.5, we can see that the gradient (m) is -3.
Finding the Y-intercept
To find where the line crosses the y-axis, we need to determine the value of y when x is 0. From the equation y = -3x - 4.5:
Set x to 0: y = -3(0) - 4.5
The y-intercept is y = -4.5
Therefore, the line crosses the y-axis at the point (0, -4.5).