4)) The equation for line j can be written as y=(1)/(8)x+7 . Parallel to line j is line k, which passes through the point (-3,-1) . What is the equation of line k?

To find the equation of line k, 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 k is parallel to line j, it will have the same slope as line j. The slope of line j is $\frac{1}{8}$, so the slope of line k is also $\frac{1}{8}$.<br /><br />Now we can substitute the values into the point-slope form:<br /><br />$y - (-1) = \frac{1}{8}(x - (-3))$<br /><br />Simplifying this equation gives us:<br /><br />$y + 1 = \frac{1}{8}(x + 3)$<br /><br />Expanding and rearranging the equation gives us the final equation of line k:<br /><br />$y = \frac{1}{8}x + \frac{3}{8} - 1$<br /><br />Simplifying further, we get:<br /><br />$y = \frac{1}{8}x - \frac{5}{8}$<br /><br />Therefore, the is $y = \frac{1}{8}x - \frac{5}{8}$.