$\"\"$

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First find the slope of the line $\"\"$ .

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Rewrite the line in slope-intercept form y = mx + b, where m is slope and b is y-intercept.

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Apply addition property of equality: If a = b than a + c = b + c.

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$\"\"$ (Add 2y to each side)

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$\"\"$ (Apply additive inverse property: $\"\"$ ) $\"\"$

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Apply subtraction property of equality: If a = b than a $\"\"$ c = b $\"\"$ c.

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$\"\"$ (Subtract 6 from each side)

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$\"\"$ (Apply additive inverse property: $\"\"$ )

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$\"\"$ (Divide each side by 2)

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$\"\"$ (Cancel common terms)

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Compare the equation with slope-intercept form and find the slope of the line.

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= $\"\"$

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$\"\"$

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If two lines are perpendicular, the slope (m₁) of one line is opposite reciprocal of the second line slope (m₂). It can be represented as, $\"\"$ .

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Slope of the line perpendicular to given line is $\"\"$

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So, slope of the new line = $\"\"$ . $\"\"$

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Graph the line using given point and slope.

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1. Draw a coordinate plane.

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2. Plot the given point (4, $\"\"$ 2).

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3. Find the next point using $\"\"$ . Start at (4, $\"\"$ 2) and go down 2 units and 3 unit right, then mark a dot and label it.

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4. Draw a line through these points.

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$\"Graph$ $\"\"$

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Graph of the line passing through the point (4, $\"\"$ 2) and slope $\"\"$ is

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$\"Graph$