Final answer:
The equation of the line parallel to the given line and passing through the point (1, 1) is y = (-5/4)x + 9/4.
Step-by-step explanation:
To find the equation of a line parallel to another and passing through a given point, we need to determine two things: the slope of the parallel line and the point it passes through. Since parallel lines have the same slope, we first find the slope of the given line by using the coordinates (-4, 4) and (0, -1).
The slope (m) is calculated by the formula m = (y2 - y1) / (x2 - x1). So, m = (-1 - 4) / (0 - (-4)) = -5 / 4. Now that we have the slope of the parallel line, we can use the point-slope form of the equation to find the equation of our line.
The point-slope form is y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope. Our line passes through (1, 1), so we substitute these values into the point-slope form:
y - 1 = (-5/4)(x - 1)
Expanding this equation to get it into slope-intercept form (y = mx + b), we get:
y = (-5/4)x + 5/4 + 1
y = (-5/4)x + 9/4
This is the slope-intercept form of the equation for the line that is parallel to the line with coordinates (-4, 4) and (0, -1) and passes through the point (1,1).