Answer:
[tex]B - A = -6[/tex]
Step-by-step explanation:
Given
Point: (-7,2)
x + 3y = -5
Required
Find B- - A in Ax + By = 3
To start with; we need to calculate the slope of x + 3y = -5
[tex]x + 3y = -5[/tex]
Subtract x from both sides
[tex]x - x + 3y = -5 - x[/tex]
[tex]3y = -5 - x[/tex]
Divide both sides by 3
[tex]\frac{3y}{3} = -\frac{5}{3} - \frac{x}{3}[/tex]
[tex]y = -\frac{5}{3} - \frac{x}{3}[/tex]
The slope of the line is the coefficient of x
Slope = [tex]- \frac{1}{3}[/tex]
The question says line Ax + By = 3 is parallel to line x + 3y = -5; This means that they have the same slope of [tex]- \frac{1}{3}[/tex]
Having calculated the slope, next is to calculate the equation of the line using the following formula;
[tex]m = \frac{y - y_1}{x - x_1}[/tex]
Where m is the slope; m = [tex]- \frac{1}{3}[/tex]; [tex](x_1, y_1) = (-7,2)[/tex]
Substitute these values in the formula above; the formula becomes
[tex]-\frac{1}{3} = \frac{y - 2}{x - -7}[/tex]
[tex]-\frac{1}{3} = \frac{y - 2}{x +7}[/tex]
Cross Multiply
[tex]-1(x+7) = 3(y-2)[/tex]
Open brackets
[tex]-x - 7 = 3y - 6[/tex]
Add x to both sides
[tex]x - x - 7 = 3y - 6 + x[/tex]
[tex]-7 = 3y - 6 +x[/tex]
Add 6 to both sides
[tex]-7 + 6 = 3y -6 + 6 + x[/tex]
[tex]-1 = 3y + x[/tex]
Multipby both sides by -3
[tex]-3(-1) = -3(3y + x)[/tex]
[tex]3 = -9y - 3x[/tex]
[tex]-9y - 3x = 3[/tex]
[tex]-3x - 9y = 3[/tex]
Comparing the above to Ax + By = 3
[tex]Ax = -3x\\A = -3[/tex]
[tex]By = -9y\\B = -9[/tex]
[tex]B - A = -9 - (-3)[/tex]
[tex]B - A = -9 + 3[/tex]
[tex]B - A = -6[/tex]
