Final answer:
The equation of the line passing through the point (7, 3) and parallel to the line 4x - 7y = 9 is y = (4/7)x - 1.
Step-by-step explanation:
The question asks us to write an equation for a line that passes through the point (7, 3) and is parallel to the line represented by the equation 4x - 7y = 9. To find a parallel line, we need a line with the same slope as the original line. First, let's rewrite the given equation in slope-intercept form (y = mx + b) to calculate the slope of the original line. This is done by solving for y:
4x - 7y = 9
-7y = -4x + 9
y = (4/7)x - 9/7
The slope (m) of this line is 4/7. A line parallel to this one will have the same slope, 4/7. Using the point-slope form, y - y1 = m(x - x1), where (x1, y1) is the given point (7, 3), we get:
y - 3 = (4/7)(x - 7)
Now, we can rewrite this into slope-intercept form:
y - 3 = (4/7)x - (4/7)(7)
y = (4/7)x - 4 + 3
y = (4/7)x - 1
This is the equation of the line that passes through the point (7, 3) and is parallel to the original line.