To find an equation for a line parallel to the line -9x = -2, you need to determine the slope of the original line. The equation -9x = -2 can be rewritten as:
-9x = -2
Now, divide both sides by -9 to isolate x:
x = (-2) / (-9)
x = 2/9
So, the slope of the original line is 2/9.
Now, to find a line parallel to this line that passes through the point (-6, 3), you can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Where:
(x1, y1) is the given point (-6, 3).
m is the slope, which is 2/9.
Plug in the values:
y - 3 = (2/9)(x - (-6))
y - 3 = (2/9)(x + 6)
Now, you can simplify and rewrite this equation in standard slope-intercept form (y = mx + b):
y = (2/9)(x + 6) + 3
y = (2/9)x + (2/9)(6) + 3
y = (2/9)x + 12/9 + 27/9
y = (2/9)x + 39/9
Now, you can simplify further:
y = (2/9)x + 13/3
So, the equation for the line parallel to -9x = -2 through the point (-6, 3) is:
y = (2/9)x + 13/3