Question: Find the x-intercept and the y-intercept. Then graph the equation. \[ 2x + 21y = -6 \] Choose…

Find the x-intercept and the y-intercept. Then graph the equation.

\[ 2x + 21y = -6 \]

Choose the graph of the equation.

A. The equation has no y-intercept.

B.

C.

Solution

To find the x-intercept and y-intercept of the equation \(2x + 2y = -6\), we can follow these steps: First, find the x-intercept by setting \(y = 0\). \[ 2x + 2(0) = -6 \] Simplify: \[ 2x = -6 \] Divide by 2: \[ x = -3 \] The x-intercept is \((-3, 0)\). Next, find the y-intercept by setting \(x = 0\). \[ 2(0) + 2y = -6 \] Simplify: \[ 2y = -6 \] Divide by 2: \[ y = -3 \] The y-intercept is \((0, -3)\). The equation is a line passing through the points \((-3, 0)\) and \((0, -3)\). Based on the provided graphs, the graph with these intercepts would match the linear equation, which is graph B.