Question: Find the x-intercept and the y-intercept. Then graph the equation. 2x + 21y = -6 O B. The…

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

2x + 21y = -6

O B. The equation has no x-intercept.

Find the y-intercept. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

O A. The y-intercept is (Simplify your answer. Type an ordered pair.)

O B. The equation has no y-intercept.

Choose the graph of the equation.

O A. [Graph A]

O B. [Graph B]

O C. [Graph C]

Solution

To find the x-intercept and y-intercept of the equation \(2x + 21y = -6\), follow these steps: Find the x-intercept: Set \(y = 0\) in the equation and solve for \(x\). \[ 2x + 21(0) = -6 \] \[ 2x = -6 \] \[ x = \frac{-6}{2} \] \[ x = -3 \] The x-intercept is \((-3, 0)\). Find the y-intercept: Set \(x = 0\) in the equation and solve for \(y\). \[ 2(0) + 21y = -6 \] \[ 21y = -6 \] \[ y = \frac{-6}{21} \] \[ y = \frac{-2}{7} \] The y-intercept is \((0, -\frac{2}{7})\). These intercepts help in graphing the equation, which passes through the points \((-3, 0)\) and \((0, -\frac{2}{7})\). Check the provided graphs to determine which one matches these points.