Question

Write an equation in standard form of the horizontal line and the vertical line that pass through the point. $$(-4,4)$$

Short answer

The equation of the horizontal line is \(y = 4\) and the equation of the vertical line is \(x = -4\).

Step-by-step solution

Formulate the Equation for the Horizontal Line

For the horizontal line passing through the point (-4,4), the y-coordinate is constant. Therefore, the equation of the line is \(y = b\), where \(b\) is the y-coordinate of the given point. Here, \(b = 4\), so the horizontal line's equation that passes through (-4,4) is \(y = 4\).

Formulate the Equation for the Vertical Line

For the vertical line passing through the point (-4,4), the x-coordinate is constant. Therefore, the equation of the line is \(x = a\), where \(a\) is the x-coordinate of the given point. In this case, \(a = -4\), so the vertical line's equation that passes through (-4,4) is \(x = -4\).