Final answer:
To find a line parallel to y = 4/7x + 4 that passes through (-4, 4), we use the fact that parallel lines have identical slopes. We apply the point-slope form and the slope 4/7 with the given point to find the new equation, which is y = 4/7x + 44/7.
Step-by-step explanation:
To find the equation of the line that is parallel to the given line y = 4/7x + 4 and passes through the point (-4, 4), we need to understand that parallel lines share the same slope. Hence, our new line will have the same slope of 4/7. However, the y-intercept will be different.
To find the y-intercept of the new line, we'll use the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Substituting the given point and the slope, we get:
y - 4 = 4/7(x + 4). To find the new y-intercept, we'll distribute the slope and simplify:
- y - 4 = 4/7x + 16/7
- y = 4/7x + 16/7 + 28/7
- y = 4/7x + 44/7
The equation of the line parallel to y = 4/7x + 4 that passes through the point (-4, 4) is thus y = 4/7x + 44/7.