the line passing through point (-3,0) with slope -3/2
To find the equation of the line passing through the point (-3, 0) with a slope of -3/2, we can use the point-slope form of a linear equation.
The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Plugging in the given values, we have y - 0 = (-3/2)(x - (-3)).
This simplifies to y = (-3/2)(x + 3).
Multiplying through by 2 to eliminate the fraction, we have 2y = -3(x + 3).
Expanding, we get 2y = -3x - 9.
Finally, rearranging the equation to the standard form of a linear equation, we have 3x + 2y + 9 = 0.
Therefore, the equation of the line passing through the point (-3, 0) with a slope of -3/2 is 3x + 2y + 9 = 0.