Final answer:
The equation of the line with the specified slope of -4 and passing through point (3,7) is y = -4x + 19, which is derived by using the point-slope form of a linear equation.
Step-by-step explanation:
To write an equation for a line with a given slope and that passes through a specific point, we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through. Given the slope of -4 and the point (3, 7), we substitute these values into the equation.
Thus, our equation will look like this:
y - 7 = -4(x - 3)
Now, we simplify:
y - 7 = -4x + 12
Add 7 to both sides:
y = -4x + 12 + 7
y = -4x + 19
Therefore, the equation of the line with a slope of -4 that passes through the point (3,7) is y = -4x + 19.