The line parallel to 2x + 3y = 12 and passing through (0, 10) has the equation y = -2/3x + 10, with a slope of -2/3, preserving the parallel relationship.
To find an equation of the line parallel to 2x + 3y = 12 and passing through the point (0, 10), we can start by determining the slope of the given line. The equation 2x + 3y = 12 can be rewritten in the slope-intercept form y = mx + b, where m is the slope.
First, solve for y:
2x + 3y = 12
3y = -2x + 12
y = -2/3x + 4
So, the slope (m) is -2/3.
Since the desired line is parallel, it will have the same slope. Now, we can use the point-slope form of a line y - y1 = m(x - x1), where (x1, y1) is a point on the line.
For the line passing through (0, 10) with a slope of -2/3:
y - 10 = -2/3x
This equation can be simplified:
y = -2/3x + 10
So, the equation of the line parallel to 2x + 3y = 12 and passing through (0, 10) is y = -2/3x + 10.