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# help plz

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Find the value of B - A if the graph of Ax + By = 3  passes through the point (-7, 2) and is parallel to the graph of x + 3y = -5.

Jul 6, 2021

#1
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From x + 3y = -5, y = -x/3 - 5, so the slope of the line is -1/3. The slope of the new line is also -1/3, so y = -x/3 + B.  Pugging in x = 2 and y = -7, we get -7 = -2/3 + B, so B = -19/3.

Then the line is y = -x/3 - 19/3.  Then 3y = -x - 19, so 3y + x = -19.  We want the right-hand side to be 3, so we mutiply both sides by -3/19: -9/19*y - 3/19*x = 3.  Therefore, B - A = -19/3 - 3 = -28/3.

Jul 6, 2021
#3
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Putting the equations into slope-intercept form,

$$y = -\frac{Ax}{B} + \frac{3}{B}$$

$$y = -\frac{x}{3} - \frac{5}{3}$$

Both lines are parallel, so $$-\frac{x}{3} = -\frac{Ax}{B}$$. Simplify to find that $$\frac{A}{B} = \frac{1}{3}$$, meaning that the slope is $$-\frac{1}{3}$$.

$$y = -\frac{x}{3} + \frac{3}{B}$$

Plug in (-7, 2).

$$2 = -\frac{-7}{3} + \frac{3}{B}$$

$$6B = 7B + 9$$

$$B = -9$$

Because A and B are in ratio $$\frac{A}{B} = \frac{1}{3}$$, B = -9 and A = -3. So B - A = -9 - (-3) = -6

Jul 6, 2021
#4
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x + 3y = -5               re arrange to y = mx+b from:

y = -1/3 x - 5/3         slope = -1/3     ( parallel slope is the same)

y = -1/3 x -  b           sub in the given point to calculate 'b'

2 = -1/3 (-7) + b       shows b = - 1/3

y = -1/3 x - 1/3         multiply by 3 to get rid of fraction

3y = 3x - 3

3x -3y = 3                 then   B - A =  -3 - 3 = - 6

Jul 6, 2021