4) Line g has an equation of y=-(2)/(9)x+6 . Parallel to line g is line h, which passes through the point (3,2) . What is the equation of line h?

To find the equation of line h, 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 h is parallel to line g, it will have the same slope as line g. The slope of line g is $-\frac{2}{9}$, so the slope of line h is also $-\frac{2}{9}$.<br /><br />Now we can substitute the values into the point-slope form:<br /><br />$y - 2 = -\frac{2}{9}(x - 3)$<br /><br />Simplifying this equation, we get:<br /><br />$y - 2 = -\frac{2}{9}x + \frac{6}{9}$<br /><br />$y - 2 = -\frac{2}{9}x + \frac{2}{3}$<br /><br />Finally, we can rearrange the equation to get it in slope-intercept form:<br /><br />$y = -\frac{2}{9}x + \frac{2}{3} + 2$<br /><br />$y = -\frac{2}{9}x + \frac{2}{3} + \frac{6}{3}$<br /><br />$y = -\frac{2}{9}x + \frac{8}{3}$<br /><br />Therefore, the equation of line h is $y = -\frac{2}{9}x + \frac{8}{3}$.