Find B - A if the graph of Ax + By = 7 passes through (2,1) and is parallel to the graph of 2x - 7y = 3.
since (2,1) lies on it
2A + B = 7 or B = 7 - 2a
slope of 2x-7=3 is 2/7
slope of Ax + By = 7 is -A/B
so -A/B = 2/7
2B = -7A
2(7-2A) = -7A
14 - 4A = -7A
3A = -14
A = -14/3
B = 7-2(-14/3) = 49/3
B - A = 49/3 - (-14/3) = 21
To find B - A, we need to determine the values of A and B from the given information.
First, let's find the slope of the line 2x - 7y = 3. To do this, we rearrange the equation into slope-intercept form (y = mx + b), where m is the slope:
2x - 7y = 3
-7y = -2x + 3
y = (2/7)x - 3/7
From this equation, we can see that the slope of the line is 2/7.
Since the line Ax + By = 7 is parallel to the line 2x - 7y = 3, the slopes of the two lines will be the same. Therefore, the slope of Ax + By = 7 is also 2/7.
Now, we can use the point-slope form of a line to find the equation of Ax + By = 7. We substitute the coordinates (2,1) and the slope (2/7) into the point-slope form:
y - y1 = m(x - x1)
Where x1 = 2, y1 = 1, and m = 2/7:
y - 1 = (2/7)(x - 2)
Simplifying the equation:
y - 1 = (2/7)x - 4/7
7y - 7 = 2x - 4
2x - 7y = 7 - 4
2x - 7y = 3
From this equation, we can see that A = 2 and B = -7. Therefore, B - A = -7 - 2 = -9.
Therefore, B - A is equal to -9.