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Chapter 4: Problem 25

Find an equation of the line containing the given point with the given slope. Express your answer in the indicated form. \((-2,-1), m=4 ;\) standard form

Short Answer

Expert verified
The equation of the line containing the given point \((-2, -1)\) and with slope \(m = 4\) in standard form is: \(4x - y - 7 = 0\).

Step by step solution

01

Use the given point and slope in the point-slope form equation

Use the given point \((-2, -1)\), with coordinates \(x_1 = -2\) and \(y_1 = -1\), and the slope \(m = 4\) in the point-slope form equation: \[y - (-1) = 4(x - (-2))\]
02

Simplify the equation

Simplify the equation by addressing the double negatives: \[y + 1 = 4(x + 2)\]
03

Expand the equation

Distribute the \(4\) on the right-hand side of the equation: \[y + 1 = 4x + 8\]
04

Rewrite the equation in standard form

To rewrite the equation in standard form, move all terms involving \(x\) and \(y\) to the left-hand side: \[4x - y + 1 - 8 = 0\] Then, simplify the equation: \[4x - y - 7 = 0\]
05

Write the final answer

The equation of the line containing the given point \((-2, -1)\) and with slope \(m = 4\) in standard form is: \[4x - y - 7 = 0\]

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