Final answer:
To find the equation of the line that is parallel to 5x + 3y = 8 and passes through the point (-1, -2), we need to find the slope of the given line, and then use the point-slope form to find the equation.
Step-by-step explanation:
To find the equation of the line that is parallel to 5x + 3y = 8 and passes through the point (-1, -2), we need to find the slope of the given line.
We can rewrite the equation of the given line in slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
So, let's rearrange the given equation to get y = -5/3x + 8/3.
Since the given line is parallel to the line we want to find, the slopes of the two lines are equal.
The slope of the line we want to find is also -5/3.
Now, using the point-slope form y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope, we can substitute the values and simplify to find the equation of the line that passes through the point (-1, -2).
Therefore, the equation of the line that contains the point (-1, -2) and is parallel to the line 5x + 3y = 8 is 5x + 3y = -11 (option a).