Answer:
To find the equation of a line that passes through a given point and is parallel to a given line, we need to use the fact that parallel lines have the same slope.
The given line has a slope of 2/3, which means that any line parallel to it will also have a slope of 2/3. Therefore, the equation of the line we are looking for will have the form:
y = (2/3)x + b
where b is the y-intercept of the line. To find the value of b, we need to use the fact that the line passes through the point (3,4). Substituting this point into the equation above, we get:
4 = (2/3)(3) + b
Simplifying this equation, we get:
4 = 2 + b
Subtracting 2 from both sides, we get:
b = 2
Therefore, the equation of the line that passes through the point (3,4) and is parallel to y = (2/3)x - 1 is:
y = (2/3)x + 2
I hope this helps!