Final answer:
The correct answer for the equation of a line given the point (-2, 2) and the slope -4/7 in standard form is d. 4x + 7y = 14. This is derived by using the point-slope form and converting it to standard form.
Step-by-step explanation:
To find the equation of a line given a point and a slope, you can use the point-slope form of a linear equation and then convert it to standard form. The point-slope form is expressed as (y - y1) = m(x - x1), where (x1, y1) is the point and m is the slope of the line.
For the given point (-2, 2) and the slope -4/7, the point-slope form would be:
y - 2 = (-4/7)(x + 2)
Multiplying through gives:
y - 2 = (-4/7)x - (8/7)
Multiplying each term by 7 to eliminate the fraction and rearrange the terms to get the standard form, Ax + By = C, we get:
7y - 14 = -4x - 8
Adding 4x to both sides and adding 14 to both sides gives:
4x + 7y = 14
Therefore, the correct answer in standard form is: d. 4x + 7y = 14.