Final answer:
To write the equation in slope-intercept form of the line that passes through the given point (4, -7) and has the given slope -1/4, we substitute the values into the formula y = mx + b. By finding the value of b using the given point, we can determine the equation of the line. The correct equation is y = -1/4x - 6.
Step-by-step explanation:
To write the equation in slope-intercept form of the line that passes through the given point and has the given slope, we can use the formula y = mx + b, where m is the slope and b is the y-intercept. In this case, the given point is (4, -7) and the slope is -1/4. We can substitute these values into the formula to find the equation of the line.
Substituting the values, we get y = (-1/4)x + b. Now we can use the given point (4, -7) to find the value of b. Plugging in the x- and y-coordinates of the point into the equation, we have -7 = (-1/4)(4) + b. Solving for b, we get b = -6.
Therefore, the equation in slope-intercept form of the line that passes through the point (4, -7) with a slope of -1/4 is y = (-1/4)x - 6. So the correct answer is A. y = -1/4x - 6.