Consider the line that passes through the point \( P(-4,0) \) and has slope \( \frac{1}{2} \). Write the point-slope equation of the line. Use exact values.

To derive the point-slope equation of the line that passes through \( P(-4,0) \) with a slope of \( \frac{1}{2} \), we can utilize the point-slope formula: \( y - y_1 = m(x - x_1) \). In this case, \( m = \frac{1}{2} \), \( x_1 = -4 \), and \( y_1 = 0 \). Plugging these values into the equation gives: \[ y - 0 = \frac{1}{2}(x - (-4)) \] or \[ y = \frac{1}{2}(x + 4) \] This is how we express the line using the point-slope form! To take it a step further, you could certainly expand it to slope-intercept form, which would look like \( y = \frac{1}{2}x + 2 \). Fun, isn’t it? The slope allows for intuitive understanding of how the line is inclined, and with this form, you can easily identify where it crosses the y-axis.