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ddd [48]
2 years ago
12

OK this is another question which I need help on please please help if you can. CAUSED ME MUCH DISTRESS

Mathematics
1 answer:
r-ruslan [8.4K]2 years ago
3 0

Answer:

15 = 2x - 3y

Step-by-step explanation:

We have the two points P1(3,-3) and P2(9,1).

First, calculate the slope between those points:

slope = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - (-3)}{9 - 3} = \frac{4}{6} = \frac{2}{3}

Now simply move 3 steps from (3,-3) towards the y-axis to get the intersection with the y-axis (each step reduces x by 1 and applies the slope to the y-value):

(3,-3)

---> (2, -3 - (2/3)) = (2,-3 2/3)

---> (1, (-3 2/3) - 2/3) = (1, -4 1/3)

---> (0, (-4 1/3) - 2/3) = (0,-5)

This tells us, that our line intersects the y-axis at (0,-5).

The general form of a line is f(x) = <SLOPE> * x + <Y-VALUEATXEQUALSZERO>.

In our case: f(x) = y = (2/3)x -5.

To get it into the correct form, we simply subtract y from both sides and get:

0 = (2/3)x - y - 5

To get only integers just multiply everything with 3 and add 15 and get:

15 = 2x - 3y, which fulfils the form asked for in the problem.

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\huge\mathscr{\colorbox{blue}{\color{yellow}{Answer:}}}

\large{\rightarrow{6\:(x\:+\:4)\:=\:-\:2\:(4x\:-\:4)\:+\:8x}}

\large{\rightarrow{6\:(x\:+\:4)\:=\:-\:2\:(4x\:-\:4)\:+\:8x}}

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<h3>1)</h3>

• 6x -2(x -5) = -2 . . . . given

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<h3>2)</h3>

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• 11x -10 +10 = 34 +10 . . . . addition property of equality

• 11x = 44 . . . . . . . . simplify

• 11x/11 = 44/11 . . . division property of equality

• x = 4 . . . . . . . . . . . simplify

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