Answer & Explanation.
To write the equation of a line with a given slope that passes through a specific point, we can use the point-slope formula, which is given by:
y - y1 = m(x - x1)
where (x1, y1) is the coordinates of the given point, and m is the slope of the line. In this case, the coordinates of the given point are (-6, 1) and the slope of the line is 4/3. Plugging these values into the point-slope formula, we get:
y - 1 = (4/3)(x + 6)
We can now rearrange the terms in this equation to get it in the form Ax + By = C, which is:
y = (4/3)x + (4/3)(-6) + 1
This equation can be rewritten as:
4x + 3y = -8
So, the equation of the line in the form Ax + By = C is 4x + 3y = -8.