Final answer:
To find the equation of a line parallel to 2x - y = 4 that passes through the point (3, 7), first determine the slope of the given line (which is 2), and then use the point-slope formula with the given point to obtain the equation: y = 2x + 1.
Step-by-step explanation:
The equation of a line that passes through the point (3, 7) and is parallel to the line 2x - y = 4 can be found by ensuring that the slope of the new line is the same as that of the given line. First, we convert the equation of the given line to slope-intercept form (y = mx + b) to identify the slope.
Rearrangement of 2x - y = 4:
2x - 4 = y
or
y = 2x - 4
From this form, we can see that the slope (m) is 2. Since parallel lines have the same slope, the slope of the new line will also be 2. Using the slope-point formula (y - y1 = m(x - x1)), where (x1, y1) = (3, 7) is the given point, we can find the equation of the line:
y - 7 = 2(x - 3)
Expanding this, we get:
y - 7 = 2x - 6
Add 7 to both sides to find the y-intercept(b):
y = 2x + 1
Therefore, the equation of the line parallel to 2x - y = 4 and passing through the point (3, 7) is y = 2x + 1.