Find the equation of the line through (5,7) parallel to the line 7x + 5y = 12.
Answer Details
To find the equation of a line parallel to another line, we need to use the fact that parallel lines have the same slope. The given line 7x + 5y = 12 can be rearranged into slope-intercept form, which is y = (-7/5)x + (12/5), where the slope is -7/5.
Since the line we want to find is parallel to this line, it must also have a slope of -7/5. We also know that the line passes through the point (5,7).
To find the equation of this line, we can use the point-slope form, which is y - y1 = m(x - x1), where (x1,y1) is the given point and m is the slope. Substituting in the values we know, we get:
y - 7 = (-7/5)(x - 5)
Simplifying this equation, we get:
y = (-7/5)x + (49/5)
So the equation of the line through (5,7) parallel to the line 7x + 5y = 12 is y = (-7/5)x + (49/5), which is option (A) 5x + 7y = 20.