Question

Line A passes through the points (-3,2) and (-23,54). Line B is parallel to line A and passes through the point (-8,0). Consider
the equation of line B in the form y= a (x + b), where a and b are rational numbers.

Answer 1

Answer:

Line A passes through (-3, 2) and (-23, 54)

slope of  line A will be

               $m_{A} =\frac{y_{2}-yx_{1} }{x_{2}- x_{1} } = \frac{54-2}{-23+3} = \frac{52}{20}= \frac{13}{5}$

Equation of line A will be

             $(y - y_{1}) = m_{A}(x-x_{1} )\\\\(y - 2) = \frac{13}{5}(x -(-3))\\\\(y - 2) = \frac{13}{5}(x +3))\\ \\\\5((y - 2) = 13(x +3))\\\\5y -10 = 13x + 39\\\\5y = 13x + 49$

Given line B is parallel to line A, So slope of A and B

                       $m_{A} \cdot m_{B} = 1$

 slope of line B will be

                       $\frac{13}{5}\cdot m_{B} = 1\\\\m_{B} = \frac{5}{13}$

Also given line B passes (-8, 0), therefore the equation of line B

                  $(y-y_{B}) = m_{B}(x-x_{B} )\\\\(y - 0) = \frac{5}{13}(x + 8)\\\\y = \frac{5}{13}(x+8)$

Therefore,

             $a = \frac{5}{13} \ \ and \ b = 8$