Final answer:
The equation of the line passing through the point (4,-2) with a slope of 4 is y = 4x - 18.
Step-by-step explanation:
To find the equation of the line passing through the point (4,-2) with a slope of 4, we can use the point-slope form of a line. The point-slope form is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Substituting the given values, we get y - (-2) = 4(x - 4). Simplifying, we have y + 2 = 4x - 16.
To put the equation in slope-intercept form (y = mx + b), we can isolate y by subtracting 2 from both sides, resulting in y = 4x - 18.
Therefore, the equation of the line passing through the point (4,-2) with a slope of 4 is y = 4x - 18.