Question

graphical representation of linear equations
cuemath the math expert
\\(x - 2y = 2\\)
\\((-2, -2)\\)
\\((0, -1)\\)
\\((2, 0)\\)
\\((4, 1)\\)

Explanation:

Identify the given line

The image shows a line labeled \(x - 2y = 2\).

Identify key points

We observe four plotted points on the line:

• \((-2, -2)\)
• \((0, -1)\)
• \((2, 0)\)
• \((4, 1)\)

Verify the equation

Substitute \((2,0)\) into the equation:

$$2 - 2(0) = 2$$

This confirms the line is \(x - 2y = 2\).

Find the intercepts

• The \(y\)-intercept is \((0, -1)\).
• The \(x\)-intercept is \((2, 0)\).

Answer:

The graph represents the linear equation:

$$x - 2y = 2$$

Key points plotted on the line include:

• \(x\)-intercept: \((2, 0)\)
• \(y\)-intercept: \((0, -1)\)
• Additional points: \((-2, -2)\) and \((4, 1)\)