Answer:
[tex]y = - \frac{4}{3} x + 2[/tex]
Step-by-step explanation:
It was stated that Line V which passes through the point (6 , 6) and is perpendicular to the graph of
[tex]y = \frac{3}{4} x - 11[/tex]
Since line V is perpendicular to this graph it means that line V's gradient is the negative inverse of this graphs' gradient. The gradient of the graph is
[tex] \frac{3}{4} [/tex]
Hence the gradient of line v is: (let the gradient of line v be x)
[tex] \frac{3}{4}x = - 1 \\ x = \frac{ - 1}{ \frac{3}{4} } \\ x = - 1 \times \frac{4}{3} \\ x = - \frac{4}{3} [/tex]
Therefore the gradient of line V is - 4/3. Since line W is parallel to line V, it would have the same gradient which is -4/3. The question also stated that line W passes through the point (-6 , 10). Therefore
[tex]x = - 6 \: \: \: \: \: y = 10 \: \: \: \: m = - \frac{4}{3} \\ y = mx + c \\ 10 = - \frac{4}{3} ( - 6) + c \\ 10 = 8 + c \\ 10 - 8 = c [/tex]
[tex]2 = c \\ equ \: of \: line \: w \: is \: y = - \frac{4}{3} x + 2[/tex]
