Problem 26 - Understanding Elementary Algebra with Geometry

Question

Sketch the graph of the given equation. Label the intercepts. $$x+y=-2$$

Step-by-Step Solution

Answer

The x-intercept is -2 and the y-intercept is -2.

Step 1: Rewrite the Equation in Slope-Intercept Form

The given equation is \(x + y = -2\). To rewrite it in slope-intercept form \((y = mx + b)\), solve for \(y\): \(-2 - x = y\). This simplifies to \(y = -x - 2\).

Step 2: Find the Y-Intercept

To find the y-intercept, set \(x = 0\) in the equation \(y = -x - 2\). \(y = -0 - 2 = -2\). So, the y-intercept is \(-2\).

Step 3: Find the X-Intercept

To find the x-intercept, set \(y = 0\) in the equation \(x + y = -2\). This gives \(x + 0 = -2\). So, the x-intercept is \(-2\).

Step 4: Plot the Intercepts on the Graph

Plot the points \((0, -2)\) and \((-2, 0)\) on the graph. These are the intercepts found in steps 2 and 3.

Step 5: Draw the Line

Draw a straight line through the points \((0, -2)\) and \((-2, 0)\) to represent the equation \(x + y = -2\).

Step 6: Label the Intercepts

Label the points \((0, -2)\) as the y-intercept and \((-2, 0)\) as the x-intercept on the graph.

Key Concepts

Slope-Intercept Form

In algebra, the slope-intercept form of a linear equation makes it easy to graph the line. The form is written as: \(y = mx + b\), where:

• \