Questions: Graph the linear equation by finding and plotting its intercepts. x-y=2 Use the graphing tool to graph the equation. Use the intercepts when drawing the line. If only one intercept exists, use it and another point to draw the line.

Graph the linear equation by finding and plotting its intercepts.
x-y=2

Use the graphing tool to graph the equation. Use the intercepts when drawing the line. If only one intercept exists, use it and another point to draw the line.

Transcript text: Graph the linear equation by finding and plotting its intercepts. \[ x-y=2 \] Use the graphing tool to graph the equation. Use the intercepts when drawing the line. If only one intercept exists, use it and another point to draw the line.

Solution

Solution Steps

Step 1: Find the x-intercept

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

\[ x - 0 = 2 \implies x = 2 \]

The x-intercept is \( (2, 0) \).

Step 2: Find the y-intercept

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

\[ 0 - y = 2 \implies y = -2 \]

The y-intercept is \( (0, -2) \).

Step 3: Write the equation in slope-intercept form

Rearrange the equation \( x - y = 2 \) to the form \( y = mx + b \).

\[ y = x - 2 \]

Final Answer

The intercepts are \( (2, 0) \) and \( (0, -2) \). The equation in slope-intercept form is \( y = x - 2 \).

{"axisType": 3, "coordSystem": {"xmin": -3, "xmax": 3, "ymin": -3, "ymax": 3}, "commands": ["y = x - 2"], "latex_expressions": ["$y = x - 2$"]}

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