Final answer:
The equation of the line that is parallel to 6x-5y=5 and passes through the point (-6,3) is y=(6/5)x+51/5.
Step-by-step explanation:
To find the equation of a line that is parallel to the given line 6x-5y=5 and also passes through the point (-6,3), we must ensure that the two lines have the same slope. We can first rewrite the given line's equation in slope-intercept form to identify its slope.
Rewriting 6x - 5y = 5 as y = mx + b, where m represents the slope, we get:
5y = 6x - 5
y = (6/5)x - 1
The slope of the given line is therefore 6/5. Since parallel lines have the same slope, our new line will have this same slope. Using the point-slope form of a line equation, which is y - y1 = m(x - x1), where (x1, y1) is a given point on the line, we can substitute the slope (m=6/5) and the point (-6,3):
y - 3 = (6/5)(x + 6)
To find the equation in slope-intercept form, we simplify:
y - 3 = (6/5)x + (6/5)*6
y = (6/5)x + 36/5 + 3
y = (6/5)x + 51/5
This is the equation of the line that is parallel to 6x-5y=5 and passes through the point (-6,3).