Final answer:
To find the equation of a line that is parallel to another line, find the slope of the given line using the formula m = (y2 - y1)/(x2 - x1). Use the point-slope form of a line and substitute the slope and a point on the line to get the equation.
Step-by-step explanation:
To find the equation of a line that is parallel to another line, we need to find the slope of the given line first. The slope of a line can be found using the formula:
m = (y2 - y1)/(x2 - x1)
Using the coordinates given, (-2, 3) and (4, -1), the slope is:
m = (-1 - 3)/(4 - (-2)) = -4/6 = -2/3
Since the line we're looking for is parallel to the given line, it will have the same slope of -2/3. Now, we can use the point-slope form of a line to find the equation:
y - y1 = m(x - x1)
Substituting the coordinates of the given point (3, 4) and the slope -2/3 into the equation, we get:
y - 4 = (-2/3)(x - 3)
Finally, we can simplify the equation to get the final answer:
y = -2/3x + 18/3 + 4 = -2/3x + 22/3