Answer: B. y = 2/3 x - 13/3
Step-by-step explanation:
two lines are said to be parallel if they have the same slope.
To find the slope of line K we will use the formula fro calculating slope which is :
m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]x_{1}[/tex] = 2
[tex]x_{2}[/tex] = 8
[tex]y_{1}[/tex] = -3
[tex]y_{2}[/tex] = 1
substituting into the values into the formula , we have :
m = [tex]\frac{1-(-3)}{8-2}[/tex]
m = [tex]\frac{4}{6}[/tex]
m = [tex]\frac{2}{3}[/tex]
Therefore : the slope of line K = [tex]\frac{2}{3}[/tex] , this means that any line that will be parallel to K must have a gradient of [tex]\frac{2}{3}[/tex].
The only line that has a gradient of [tex]\frac{2}{3}[/tex] is the line y = 2/3x - 13/ 3 ,this means that the line is parallel to Line K
