Question

Write an equation for a line perpendicular to y=5x+1 and passing through the points (5,-2)

Answer 1

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$\text{\textbf{Hello!} In this question, we are trying to find the equation of a line}\\\text{that is \underline{perpendicular} to our given equation}$
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$\textbf{Explanation:}\\\\\text{To help us answer our question, we need to note some of our given info:}\\\\\text{Equation: y = 5x + 1}\\\\\text{Point passed through: (5, -2)}\\\\\text{We can use the above information to help us find our perpendicular equation.}\\\\\text{We will be using the slope-intercept form equation to help get us our answer:}\\\\\text{y = mx + b}$

$\text{When a line is perpendicular to an equation, it means that its slope is }\\\text{\textbf{opposite} which results in the lines to meet at a \underline{90-degree} angle.}$
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$\textbf{Solve:}\\\\\text{To get our perpendicular slope, we will use the formula:}\\\\\text{m1 = }-\frac{1}{m2}\\\\\text{m1 will be our given slope (5) and m2 will be our already provided slope. }\\\\\text{This is also known as a \underline{negative reciprocal}. }\\\\\text{Therefore: m1 = }-\frac{1}{5}\\\\\text{Since we now know our slope, we can plug it into our "m" variable in the}\\\text{slope intercept equation:}\\\\\text{y = }-\frac{1}{5}x+b$

$\text{To find where the point is on the y-intercept, we will plug in our point}\\\text{(5, -2) to it's corresponding spots in our new equation above.}\\\\\text{Plug "5" to x and "-2" to y and solve:}\\\\\text{-2 = }-\frac{1}{5}(5)+b\\\\\text{-2 = }-1+b\\\\\text{Add 1 to both sides.}\\\\\text{-1 = }b\\\\\text{Therefore, our y-intercept is -1.}$
$\text{When we plug -1 into our new equation, we get:}\\\\\text{y = }-\frac{1}{5}x-1\\\\\text{Therefore, our perpendicular equation is: }\boxed{y = -\frac{1}{5}x-1}$
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$\textbf{Answer:}\\\\\boxed{y = -\frac{1}{5}x-1}$
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$\textbf{Additional Info:}\\\\\text{You can learn more about \textbf{slope-intercept form} below:}$
https://brainly.com/question/27985430
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