Final answer:
The equation of the line with a slope of -4 through the point (5,-1) is written as y = -4x + 19, which represents a straight line with a negative slope.
Step-by-step explanation:
To write the equation of a line with a slope of -4 through the point (5,-1), we use the point-slope form of a line's equation: y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point. Substituting the given values into the formula, we get:
y - (-1) = -4(x - 5)
Simplify to get the equation in slope-intercept form, y = mx + b:
y + 1 = -4x + 20
Subtract 1 from both sides to solve for y:
y = -4x + 19
This equation represents a straight line with a negative slope, which means it moves downward on the graph as the x-value increases.