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kirza4 [7]
3 years ago
11

WILL MARK BRAINLIEST!!! :)

Mathematics
1 answer:
Vilka [71]3 years ago
3 0

Answer:

A) y = 1/3x + 4

B) y = 1/2x - 9

Step-by-step explanation:

A) In order to find this, we must first solve the initial equation for y to get the slope.

-x + 3y = 6

3y = x + 6

y = 1/3x + 2

Now we know the slope to be 1/3 since parallel lines have the same slope. So we take this slope and the point and use point-slope form to find the equation.

y - y1 = m(x - x1)

y - 5 = 1/3(x - 3)

y - 5 = 1/3x - 1

y = 1/3x + 4

B) To find this line, we again have to find the slope of the initial equation by solving for y.

2x + y = -4

y = -2x - 4

Now we know our new slope to be 1/2. This is because perpendicular lines have opposite and reciprocal slopes. We can use this and the point to solve in the same way.

y - y1 = m(x - x1)

y - - 8 = 1/2(x - 2)

y + 8 = 1/2x - 1

y = 1/2x - 9

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y=\frac{1}{3}x-2

<u>Statements</u>

<u>case A)</u> The graph is a straight line.

The statement is True

Because, this is a linear equation (see the attached figure)

<u>case B)</u> The line passes through the origin.

The statement is False

Because the point (0,0) is not a solution of the equation

Verify

Substitute the value of x and y in the equation

0=\frac{1}{3}*0-2

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the point (0,0) is not a solution

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The line does not pass through the origin

<u>case C)</u> The line passes through the point  (0,-2)

The statement is True

Because the point (0,-2) is a solution of the equation

Verify

Substitute the value of x and y in the equation

-2=\frac{1}{3}*0-2

-2=-2 ------> is true

the point (0,-2) is a solution

therefore

The line passes through the point (0,-2)

<u>case D) </u>The slope of the line is 3

The statement is False

Because, the slope of the line is m=\frac{1}{3}

<u>case E)</u> The y-intercept of the line is 2

The statement is False

we know that

The y-intercept is the value of y when the value of x is equal to zero

so

For x=0

find the value of y

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the y-intercept is equal to -2


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