Final answer:
To find a line parallel to the given line 6x + 3y = 1 and passing through the point (-5, -4), we need to determine the slope of the given line and use the point-slope form of a linear equation.
Step-by-step explanation:
To find a line parallel to the given line, we need to determine the slope of the given line. The equation of the given line is 6x + 3y = 1. We need to rearrange this equation to get it in slope-intercept form of y = mx + b, where m is the slope and b is the y-intercept. Rearranging the equation, we get y = -2x + 1/3. Therefore, the slope of the given line is -2.
Since we want to find a line parallel to this line and passing through the point (-5, -4), we know that the slope of the new line will also be -2. Using the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope, we can substitute the values and solve for the new line. Substituting (-5, -4), we get y - (-4) = -2(x - (-5)). Simplifying this equation, we get y + 4 = -2(x + 5), which can be further simplified to y = -2x - 14.
Therefore, the line that passes through the point (-5, -4) and is parallel to the line 6x + 3y = 1 is y = -2x - 14.