(1) The equation for line c can be written as y=(3)/(4)x-2 Line d, which is perpendicular to line c, includes the point (6,-3) . What is the equation of line d?

To find the equation of line d, we need to determine its slope and use the point-slope form of a linear equation.<br /><br />Step 1: Find the slope of line c.<br />The slope of line c is given by the coefficient of x in the equation $y=\frac {3}{4}x-2$. Therefore, the slope of line c is $\frac {3}{4}$.<br /><br />Step 2: Find the slope of line d.<br />Since line d is perpendicular to line c, its slope is the negative reciprocal of the slope of line c. Therefore, the slope of line d is $-\frac {4}{3}$.<br /><br />Step 3: Use the point-slope form to write the equation of line d.<br />The point-slope form of a linear equation is given by $y-y_1=m(x-x_1)$, where $(x_1,y_1)$ is a point on the line and m is the slope. Using the point $(6,-3)$ and the slope $-\frac {4}{3}$, we can write the equation of line d as:<br />$y-(-3)=-\frac {4}{3}(x-6)$<br /><br />Step 4: Simplify the equation.<br />Simplifying the equation, we get:<br />$y+3=-\frac {4}{3}(x-6)$<br />$y+3=-\frac {4}{3}x+8$<br />$y=-\frac {4}{3}x+5$<br /><br />Therefore, the equation of line d is $y=-\frac {4}{3}x+5$.