Final answer:
The equation of a line parallel to y = 2/3x – 7 and passing through the point (-3, 1) is y = 2/3x + 3. This is found by using the point-slope form with the given point and the slope of the original line.
Step-by-step explanation:
To write the equation of a line that is parallel to a given line and passes through a specific point, you must follow these steps:
- Identify the slope of the given line.
- Use the same slope for the new line, since parallel lines have equal slopes.
- Apply the point-slope form with the given point and the slope.
In this case, the given line is y = 2/3x – 7. The slope (m) of this line is 2/3.
The point given is (-3, 1). Using the point-slope form, which is y - y1 = m(x - x1), where (x1, y1) is the given point, we can substitute m = 2/3 and (x1, y1) = (-3, 1):
y - 1 = 2/3(x + 3).
To find the y-intercept, expand and simplify this equation:
y - 1 = 2/3x + 2
y = 2/3x + 3
This is the equation of the line that is parallel to y = 2/3x – 7 and passes through the point (-3, 1).