To find the equation of a line that is parallel to another line, we first need to know the slope of the original line. The given line is y = 2x + 1, which is already in slope-intercept form (y = mx + b), where m is the slope.
From the equation y = 2x + 1, we can see that the slope (m) is 2.
Since parallel lines have the same slope, the line we are looking for will also have a slope of 2 and must pass through the point (1, 4).
We can use the point-slope form of the equation of a line, which is given by:
y – y1 = m(x – x1)
Here, (x1, y1) is the point on the line, which is (1, 4), and m is the slope.
Substituting the values:
y – 4 = 2(x – 1)
Now we can simplify this equation:
y – 4 = 2x – 2
y = 2x + 2
So, the equation of the line that passes through the point (1, 4) and is parallel to y = 2x + 1 is:
y = 2x + 2