To write the equation of a line that is parallel to a given line and passes through a specific point (let’s denote it as point C), you need to follow these steps:
- Identify the slope of the given line:
The equation of a line is commonly expressed in the slope-intercept form, which is:y = mx + b, wheremindicates the slope. If your given line is not in this form, you may need to manipulate it to find the slope. - Use the same slope for the parallel line:
Parallel lines share the same slope. Therefore, once you identify the slopemof the given line, use this same slope for your new line. - Insert the coordinates of point C:
Let’s assume point C has coordinates(x_0, y_0). With the known slope and the point C, we’ll employ the point-slope form of the equation of a line, which is given by:
y - y_0 = m(x - x_0) - Rewrite it in your desired form:
You can rearrange the point-slope form to standard form (Ax + By = C) or slope-intercept form (y = mx + b) as needed.
Example:
Assume the given line’s equation is y = 2x + 3 and point C is (1, 4).
- The slope
mof the given line is2. - Using the point-slope form with point C and the slope:
y - 4 = 2(x - 1) - Expanding it gives us:
y - 4 = 2x - 2 - And rearranging to slope-intercept form results in:
y = 2x + 2
So the equation of the line parallel to the original line and passing through point C is y = 2x + 2.