Answer: The equation of the line that passes through the point (1, 3) and is parallel to the line 2x - y = 4 is y = 2x - 1.
Explanation:
To find the equation of the line that is parallel to 2x - y = 4 and passes through the point (1, 3), we first need to find the slope of the given line. We can rearrange the equation of the line into slope-intercept form y = mx + b, where m is the slope and b is the y-intercept:
2x - y = 4
-y = -2x + 4
y = 2x - 4
Therefore, the slope of the given line is 2.
Since we want to find the equation of a line that is parallel to this line, it will have the same slope of 2. We can use the point-slope form of a linear equation to write the equation of the line:
y - y1 = m(x - x1)
where (x1, y1) is the given point (1, 3) and m is the slope of the line, which is 2. Substituting these values, we get:
y - 3 = 2(x - 1)
Expanding and simplifying, we get:
y = 2x - 1
Therefore, the equation of the line that passes through the point (1, 3) and is parallel to the line 2x - y = 4 is y = 2x - 1.