Final answer:
The equation of the line parallel to y = 3x – 2 that passes through the point (1, –2) is y = 3x – 5, which is found by using the slope of 3 from the given line and the point to solve for the y-intercept.
Step-by-step explanation:
The equation of the line that is parallel to y = 3x – 2 and passes through the point (1, –2) can be found by using the fact that parallel lines have the same slope. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. Since the given line has a slope of 3, our line must also have a slope of 3. Now, we use the point that the line passes through to find the y-intercept (b).
We substitute x with 1 and y with –2 into the slope-intercept equation:
y = mx + b–2 = (3)(1) + b–2 = 3 + b
To find b, subtract 3 from both sides:
b = –2 – 3b = –5
Therefore, the equation of the line in slope-intercept form is y = 3x – 5.