Question

use your knowledge of \\(x\\)- and \\(y\\)-intercepts to choose the correct graph of the equation.
\\5x - 2y = 10\\
enter the appropriate letter for the graph.

Explanation:

Find the x-intercept

To find the \(x\)-intercept of the linear equation, we set \(y = 0\) and solve for \(x\).

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$$

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

Find the y-intercept

To find the \(y\)-intercept of the linear equation, we set \(x = 0\) and solve for \(y\).

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$$

The \(y\)-intercept is at the point \((0, -5)\).

Match intercepts to the correct graph

We look for the graph that crosses the \(x\)-axis at \(2\) and the \(y\)-axis at \(-5\).

• Graph a: \(x\)-intercept is at \(2\), \(y\)-intercept is at \(5\).
• Graph b: \(x\)-intercept is at \(2\), \(y\)-intercept is at \(-5\).
• Graph c: \(x\)-intercept is at \(-2\), \(y\)-intercept is at \(-5\).
• Graph d: \(x\)-intercept is at \(-2\), \(y\)-intercept is at \(5\).

Therefore, graph b is the correct representation.

Answer:

• a
• b (Correct answer)
• c
• d