Final answer:
The equation of the line passing through (-4, -6) with a slope of 5/4 in the form Ax + By = C is 5x - 4y = 4.
Step-by-step explanation:
To find the equation of a line in the form Ax + By = C, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope.
In this case, the point is (-4, -6) and the slope is 5/4.
Substituting these values into the equation gives us:
y - (-6) = (5/4)(x - (-4))
y + 6 = (5/4)(x + 4)
Next, we can multiply both sides of the equation by 4 to get rid of the fraction:
4y + 24 = 5(x + 4)
Expanding the right side gives us:
4y + 24 = 5x + 20
Now, we can rearrange the equation in the form Ax + By = C:
5x - 4y = 4
So, the correct answer is 5x - 4y = 4 (option b).