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10. Find an equation of the line passing through the point (-2,2) that is perpendicular to the line y=-(4)/(3)x-6 square Do not use decimal approximations in your answer. Practice similar Help me with this

Pergunta

10.
Find an equation of the line passing through the point (-2,2) that is perpendicular to the line y=-(4)/(3)x-6
square 
Do not use decimal approximations in your answer.
Practice similar
Help me with this

10. Find an equation of the line passing through the point (-2,2) that is perpendicular to the line y=-(4)/(3)x-6 square Do not use decimal approximations in your answer. Practice similar Help me with this

Solução

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GabriellaElite · Tutor por 8 anos

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<p> y = 3x + 8</p>

Explicação

<p> <br />1. The slope of the given line \(y = -\frac{4}{3}x - 6\) is \(-\frac{4}{3}\).<br />2. The slope of a line perpendicular to this line would be the negative reciprocal of \(-\frac{4}{3}\), which is \(3\).<br />3. Using the point-slope form of a line, \(y - y_1 = m(x - x_1)\), where \(m\) is the slope and \((x_1, y_1)\) is a point on the line, we can plug in the given point (-2,2) and the slope \(3\).<br />4. This gives: \(y - 2 = 3(x + 2)\).<br />5. Simplifying, we get the equation of the line as \(y = 3x + 8\).<br /></p>
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