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).