Write the equation of a line that passes through the point (2,3) and is parallel to 3y + 2x = 7
To find the equation of a line parallel to 3y + 2x = 7, first convert the given equation into slope-intercept form, which is y = mx + b:
3y + 2x = 7
3y = -2x + 7
y = (-2/3)x + 7/3
Since the new line is parallel, it will have the same slope as the given line, which is (-2/3). We can substitute the point (2, 3) into the point-slope form of a line, which is y - y1 = m(x - x1):
y - 3 = (-2/3)(x - 2)
Now, let's simplify this equation:
y - 3 = (-2/3)x + 4/3
To get the equation in slope-intercept form, let's isolate y:
y = (-2/3)x + 4/3 + 3
Finally, let's simplify and write the equation in its final form:
y = (-2/3)x + 4/3 + 9/3
y = (-2/3)x + 13/3