Which of the following is the slope-intercept form of the equation of

The slope-intercept form of the equation of a straight line is given by y = mx + c, where,
m = Slope of the line
c = y-intercept of the line

Note that, in the slope-intercept form, the coefficient of y is always 1 and the coefficient of x represents the slope of the line.

When two lines, whose slopes are \(m_1\) and \(m_2\) respectively, are perpendicular to each other,
\(m_1\) * \(m_2\) = -1

For the line y = 2x + 3, slope = coefficient of x = 2. Let this be \(m_1\).

Let the slope of the line, whose equation is to be found, be m2. Since this line is perpendicular to the line y = 2x + 3,
\(m_1\) * \(m_2\) = -1

Substituting the value of \(m_1\) = 2, we have,
2 * \(m_2\) = -1

Simplifying, we have \(m_2\) = -\(\frac{1}{2}\).

The equation of the line should be of the form, y = -\(\frac{1}{2}\)x + c. Based on this, answer options A, D and E can be eliminated.

Since the line passes through the point (4,0), the coordinates of the point can be substituted in the equation of the line, to find out the value of c.

Substituting, we have,

0 = -\(\frac{1}{2}\) * 4 + c

0 = -2 + c

c = 2

Therefore, the equation of the line is y = -\(\frac{1}{2}\)* x + 2.

The correct answer option is B.