Question

Use the equation \(2 x+7 y=14\). What is the \(y\) -intercept?

Short answer

The y-intercept of the equation \(2x + 7y = 14\) is 2.

Step-by-step solution

Understand the problem

The equation given is \(2x + 7y = 14\). The goal is to find the y-intercept, which is the point where the line crosses the y-axis. This occurs when \(x = 0\).

Substitute \(x = 0\) into the equation

Substitute \(x = 0\) into the equation \(2x + 7y = 14\) to find \(y\). The equation becomes \(2(0) + 7y = 14\) which simplifies to \(7y = 14\).

Solve for \(y\)

Solve the equation \(7y = 14\) for \(y\) by dividing both sides by 7. The solution is \(y = 14 / 7 = 2\). Therefore, the y-intercept is 2.