Question

Find in Point-Slope Form, the equation parallel to y = 1/2x-3 and goes through the point (6.-3).

Answer 1

To find the equation of a line parallel to y = 1/2x - 3 that passes through (6, -3), use the slope of the given line (1/2) in the point-slope formula to obtain y + 3 = 1/2x - 3.

Step-by-step explanation:

To find an equation of a line parallel to y = 1/2x - 3 that goes through the point (6, -3) in point-slope form, we need to follow these steps:

1. Identify the slope (m) of the given line. Since the equation is in the form y = mx + b, where m is the slope, the slope of the original line is 1/2.
2. Understand that parallel lines have the same slope. Therefore, the new line will also have a slope of 1/2.
3. Apply the point-slope formula y - y1 = m(x - x1), where (x1, y1) is the point the line passes through, and m is the slope of the line. In this case, (x1, y1) = (6, -3) and m = 1/2.
4. Substitute the point and the slope into the point-slope formula: y - (-3) = (1/2)(x - 6), which simplifies to y + 3 = 1/2x - 3.

Thus, the point-slope form of the equation for the line parallel to y = 1/2x - 3 that goes through the point (6, -3) is y + 3 = 1/2x - 3.