Question

select the correct answer. what is the y-intercept of the line 2x + 3y = 6? a. (0,2) b. (2,0) c. (0,3) d. (3,0)

Explanation:

Step1: Recall y - intercept definition

The y - intercept of a line is the point where the line crosses the y - axis. At the y - axis, the x - coordinate is 0. So we substitute \(x = 0\) into the equation of the line \(2x+3y = 6\).

Step2: Substitute \(x = 0\) into the equation

Substitute \(x = 0\) into \(2x + 3y=6\), we get \(2(0)+3y=6\), which simplifies to \(3y = 6\).

Step3: Solve for y

To solve for \(y\), divide both sides of the equation \(3y = 6\) by 3. So \(y=\frac{6}{3}=2\).
Since \(x = 0\) and \(y = 2\), the y - intercept is the point \((0,2)\).

Answer:

A. \((0,2)\)