Final answer:
To find a line parallel to another line and passing through a given point, use the point-slope form, y - y1 = m(x - x1), where (x1, y1) are the given point's coordinates and m is the slope from the first line's equation.
Step-by-step explanation:
To find a line passing through a point and parallel to another line, you can use the point-slope form of the equation. First, determine the slope of the given line, which is the coefficient of x in the slope-intercept form y = a + bx. Then, use the slope (b in this case) along with the coordinates of the given point to write the new line's equation in point-slope form, which is y - y1 = m(x - x1), where (x1, y1) are the coordinates of the given point and m is the slope of the parallel line. Since parallel lines have the same slope, this will ensure the two lines are parallel.
For example, if the given line equation is y = 2x + 3 and it passes through the point (4, 5), the slope is 2. The equation of a line parallel to the given line and passing through (4, 5) would be y - 5 = 2(x - 4).