Question

Find the slope and the y-intercept of the line. $$y=-4 x+\frac{1}{2}$$

Short answer

The slope of the line is -4, and the y-intercept is \( \frac{1}{2} \).

Step-by-step solution

Identify the given equation

The given equation is \(y = -4x + \frac{1}{2}\). This equation is in the form of a linear equation \(y = mx + b\), where \(m\) represents the slope of the line and \(b\) represents the y-intercept.

Identify the slope

Now compare the given equation, \(y = -4x + \frac{1}{2}\), with the standard form, \(y = mx + b\). The term that multiplies the x in the equation is the slope \(m\). Here, \(m = -4\). Therefore, the slope of the line is -4.

Identify the y-intercept

Looking at the given equation, \(y = -4x + \frac{1}{2}\), the y-intercept is given as \(b = \frac{1}{2}\), which is the constant term. Therefore, the y-intercept of the line is \(\frac{1}{2}\).