The problem asks to find the equation of a line passing through the point $(-1, 4)$ with a slope of $-3$.

We can use the point-slope form of a linear equation: $y - y_1 = m(x - x_1),$ where $(x_1, y_1)$ is a point on the line and $m$ is the slope.

Step-by-step Solution:

1. Substitute the given slope $m = -3$ and the point $(-1, 4)$ into the formula: $y - 4 = -3(x - (-1)).$

2. Simplify the double negative: $y - 4 = -3(x + 1).$

3. Distribute the slope $-3$: $y - 4 = -3x - 3.$

4. Add 4 to both sides to isolate $y$: $y = -3x + 1.$

Final Answer:

The equation of the line is: $y = -3x + 1.$

Would you like further clarification on this solution or additional examples?

Related Questions:

1. How do you convert the equation $y = -3x + 1$ into standard form $Ax + By = C$?
2. What is the y-intercept of the equation $y = -3x + 1$?
3. How do you find the x-intercept of the equation $y = -3x + 1$?
4. How would you graph the line $y = -3x + 1$?
5. What is the general form of a line, and how does it differ from point-slope form?

Tip:

When working with slope-intercept or point-slope forms, always double-check your slope ($m$) and the substitution of points to avoid sign errors!