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Chapter 0: Problem 23

Sketch the line through the given point with the indicated slope. $$ (-1,-2) ; \quad-1 $$

Short Answer

Expert verified
The line that passes through the point \((-1, -2)\) with a slope of -1 can be represented by the equation \(y = -x - 3\). To sketch the line, plot the given point and the y-intercept \((0, -3)\) on the coordinate plane and draw a line through these points while maintaining a slope of -1.

Step by step solution

01

Identify the slope and given point.

In this problem, the given slope \(m\) is -1, and the given point is \((-1, -2)\).
02

Calculate the value of "b" using the line equation.

Since the point \((-1, -2)\) lies on the line, we can substitute the x and y values into the equation, \(y = m \cdot x + b\), and solve for \(b\). \[ -2 = -1 \cdot (-1) + b \] \[ -2 = 1 + b \] \[ -3 = b \] So, the value of \(b\) is -3.
03

Write the line equation with the slope and y-intercept values.

Now that we have the value of \(b\), we can write the complete equation for the line: \[ y = -x - 3 \]
04

Sketch the line on the coordinate plane.

To sketch the line, first plot the given point \((-1, -2)\) and the y-intercept \((0,-3)\) on the coordinate plane. Then, draw a line through these points while keeping the slope of -1. Remember that a slope of -1 means that the line goes down by 1 unit for every unit moved to the right. So, starting at either point, you can continue plotting points on the line by following this pattern (moving down one and to the right one). Make sure the line passes through the given point \((-1,-2)\) and has a slope of -1. This will give you a visual representation of the line described by the equation \(y = -x - 3\).

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