Which of the following is a correct equation for the line passing through the point (-1,4) and having slope m = -3?

A. y-4=-3(x+1)

B. y=-3x+1

C. 3x+y=1

D. y=-1/4x-3

To find the correct equation, we will use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) represents a point on the line and m is the slope of the line.

The given point is (-1,4), and the slope is m = -3.

Substituting the values into the point-slope form equation:
y - 4 = -3(x - (-1))

Simplifying the equation:
y - 4 = -3(x + 1)

Now, let's compare this equation with the options provided:

A. y - 4 = -3(x + 1) - The equation matches the point-slope form. This is a correct equation for the line passing through the given point (-1,4) with a slope of m = -3.

B. y = -3x + 1 - This equation is in slope-intercept form, y = mx + b, where m represents the slope, and b represents the y-intercept. The given point does not satisfy this equation.

C. 3x + y = 1 - This equation is in standard form, Ax + By = C, where A, B, and C are constants. We need to rearrange the equation to compare it with the point-slope form.

Re-arranging the equation to slope-intercept form:
y = -3x + 1 - This equation matches the slope-intercept form. However, it is not equivalent to the point-slope form for the given point.

D. y = -1/4x - 3 - This equation is in slope-intercept form, but the slope does not match the given slope of m = -3. Therefore, it is incorrect.

Therefore, the correct equation for the line passing through the point (-1,4) with a slope of m = -3 is option A, y - 4 = -3(x + 1).