The equation for line c can be written as y=-(6)/(7)x-1 . Line d is parallel to line c and passes (10,-9) . What is the equation of line d? Write the in slope-form. Write the numbers in th as simplified proper fractions,r fractions,or integers. square

To find the equation of line d, we need to use the slope-intercept form of a linear equation, which is given by:<br /><br />\[ y = mx + b \]<br /><br />where \( m \) is the slope and \( b \) is the y-intercept.<br /><br />Since line d is parallel to line c, it will have the same slope as line c. The slope of line c is given by:<br /><br />\[ m = -\frac{6}{7} \]<br /><br />Now, we need to find the y-intercept (\( b \)) of line d. We know that line d passes through the point \((10, -9)\). We can use this point to find the y-intercept by substituting the values of \( x \) and \( y \) into the slope-intercept form:<br /><br />\[ -9 = -\frac{6}{7}(10) + b \]<br /><br />Simplify the equation:<br /><br />\[ -9 = -\frac{60}{7} + b \]<br /><br />To isolate \( b \), we need to add \( \frac{60}{7} \) to both sides of the equation:<br /><br />\[ -9 + \frac{60}{7} = b \]<br /><br />Convert \(-9\) to a fraction with a denominator of 7:<br /><br />\[ -9 = -\frac{63}{7} \]<br /><br />Now add the fractions:<br /><br />\[ -\frac{63}{7} + \frac{60}{7} = b \]<br /><br />\[ -\frac{3}{7} = b \]<br /><br />So, the y-intercept of line d is \(-\frac{3}{7}\).<br /><br />Now we can write the equation of line d in slope-intercept form:<br /><br />\[ y = -\frac{6}{7}x - \frac{3}{7} \]<br /><br />Therefore, the equation of line d is:<br /><br />\[ y = -\frac{6}{7}x - \frac{3}{7} \]