$\"\"$

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The line equation in slope-intercept form is $\"\"$ , where m is the slope and b is the y-intercept.

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Find the slope of the line $\"\"$

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

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$\"\"$ (Additive inverse property: $\"\"$ )

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$\"\"$ (Divide each side by 3)

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$\"\"$ (Cancel common terms)

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Slope of the line is $\"\"$ $\"\"$

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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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So, slope of the line perpendicular to equation is $\"\"$ . $\"\"$

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Substitute (x₁, y₁) = ( 4, 7) and $\"\"$ in the point-slope form equation

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$\"\"$

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$\"\"$ (Substitute (x₁, y₁) and m values)

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$\"\"$ (Apply distributive property: a(b + c) = ab + ac) \ \

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$\"\"$ (Multiply: $\"\"$ ) \ \

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$\"\"$ (Add 7 to each side)

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$\"\"$ (Additive inverse property: $\"\"$ )

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$\"\"$ (Additive identity property: $\"\"$ )

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$\"\"$ (Add: $\"\"$ ) $\"\"$

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The slope-intercept form line equation is $\"\"$ .

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