1)) The equation for line t can be written as y+8=(1)/(2)(x+7) Line u includes the point (8,10) and is parallel to line t. What is the equation of line u?

To find the equation of line u, 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 u is parallel to line t, it will have the same slope as line t. The slope of line t can be found by rearranging the equation $y+8=\frac {1}{2}(x+7)$ into slope-intercept form ($y = mx + b$), where $m$ is the slope.<br /><br />Rearranging the equation, we get:<br /><br />$y = \frac{1}{2}x + \frac{7}{2} - 8$<br /><br />Simplifying further, we have:<br /><br />$y = \frac{1}{2}x - \frac{9}{2}$<br /><br />From this equation, we can see that the slope of line t is $\frac{1}{2}$.<br /><br />Now, we can use the point-slope form to find the equation of line u. We know that line u passes through the point $(8,10)$, so we can substitute these values into the point-slope form:<br /><br />$y - 10 = \frac{1}{2}(x - 8)$<br /><br />Simplifying this equation, we get:<br /><br />$y - 10 = \frac{1}{2}x - 4$<br /><br />Finally, rearranging the equation to slope-intercept form, we have:<br /><br />$y = \frac{1}{2}x + 6$<br /><br />Therefore, the equation of line u is $y = \frac{1}{2}x + 6$.