4) The equation of line p is y=(1)/(4)x-8 Line q, which is parallel to line p includes the point (6,-3) What is the equation of line q?

To find the equation of line q, we need to use the point-slope form of a linear equation, which is given by:<br /><br />$y - y_1 = m(x - x_1)$<br /><br />where $(x_1, y_1)$ is a point on the line and $m$ is the slope of the line.<br /><br />Since line q is parallel to line p, it will have the same slope as line p. The slope of line p is $\frac{1}{4}$, so the slope of line q is also $\frac{1}{4}$.<br /><br />Now we can substitute the values of the point $(6, -3)$ and the slope $\frac{1}{4}$ into the point-slope form equation:<br /><br />$y - (-3) = \frac{1}{4}(x - 6)$<br /><br />Simplifying this equation gives us:<br /><br />$y + 3 = \frac{1}{4}x - \frac{3}{2}$<br /><br />Finally, we can rearrange the equation to get it in slope-intercept form:<br /><br />$y = \frac{1}{4}x - \frac{3}{2} - 3$<br /><br />$y = \frac{1}{4}x - \frac}{2}$<br /><br />Therefore, the equation of line q is $y = \frac{1}{4}x - \frac{9}{2}$.