Final answer:
The equation of the line parallel to 7x - 2y = -3 and passing through the point (-6,4) is y = (7/2)x + 25.
Step-by-step explanation:
To find the equation of the line that is parallel to the given line 7x - 2y = -3 and passes through the point (-6,4), we first need to determine the slope of the given line. A line with m as the slope and b as the y-intercept is expressed as y = mx + b. We can reorganize the provided line into slope-intercept form as follows:
- 7x - 2y = -3
- -2y = -7x - 3
- y = (7/2)x + 3/2
Now, we see that the slope (m) is 7/2 for the given line. A parallel line will have the same slope, so our new line will also have a slope of 7/2. The equation of the line that passes through the specified point is found using the point-slope form:
- y - y1 = m(x - x1)
- y - 4 = (7/2)(x + 6)
Expanding this and solving for y gives us:
- y - 4 = (7/2)x + 21
- y = (7/2)x + 25
Thus, the equation of the parallel line in slope-intercept form is y = (7/2)x + 25.