Questions: Finding x- and y-intercepts of a line given the equation: Basic Find the x-intercept and y-intercept of the line. 2 x-5 y=10 x-intercept: y-intercept:

Solution Steps

To find the intercepts of the line given by the equation \(2x - 5y = 10\), we follow these steps:

1. Find the \(x\)-intercept: Set \(y = 0\) in the equation and solve for \(x\).
2. Find the \(y\)-intercept: Set \(x = 0\) in the equation and solve for \(y\).

To find the \(x\)-intercept, we set \(y = 0\) in the equation \(2x - 5y = 10\). This simplifies to:

\[ 2x - 5(0) = 10 \implies 2x = 10 \]

Solving for \(x\), we divide both sides by 2:

\[ x = \frac{10}{2} = 5 \]

Thus, the \(x\)-intercept is \((5, 0)\).

To find the \(y\)-intercept, we set \(x = 0\) in the equation \(2x - 5y = 10\). This simplifies to:

\[ 2(0) - 5y = 10 \implies -5y = 10 \]

Solving for \(y\), we divide both sides by \(-5\):

\[ y = \frac{10}{-5} = -2 \]

Thus, the \(y\)-intercept is \((0, -2)\).

Final Answer