Answer:
y = 2x + 6
Explanation:
Relationship between the slopes of parallel lines:
The slopes of parallel lines are equal to each other.
This means that if we identify the slope of y = 2x - 11, we can also find the slope of the other line.
Form of y = 2x - 11:
y = 2x - 11 is in the slope-intercept form of a line, whose general equation is given:
y = mx + b, where
- m is the slope,
- and b is the y-intercept.
Thus, the slope of both y = 2x - 11 and the other line is 2.
Finding the y-intercept of the other line (b):
Since we know that the slope of the other line is 2 and that is passes through (3, 12), we can find the y-intercept (b) by substituting 2 for m and (3, 12) for (x, y) in the slope-intercept form:
12 = 2(3) + b
(12 = 6 + b) - 6
6 = b
Thus, the y-intercept (b) of the other line is 6.
Writing the equation of the other line:
Therefore, y = 2x + 6 is the equation of the line passing through the point P (3, 12).