Answer:
• Since these lines are perpendicular, their product of their gradients is negative one:
[tex] \dashrightarrow \: { \tt{m_{1} \times m _{2} = - 1 }}[/tex]
• m1 is gradient of first line.
• m2 is gradient of second line.
[tex] \dashrightarrow \: { \tt{ - \frac{1}{3} \times m_{2} = - 1}} \\ \\ \hookrightarrow \: { \underline{ \tt{ \: \: m _{2} = 3 \: \: }}}[/tex]
• since they intersect at a point on x-axis, y = 0
• Considering the first line: y = 9 - ⅓x
[tex]\dashrightarrow \: { \tt{0 = 9 - \frac{1}{3} x}} \\ \\ { \tt{x = 9 \times 3 = 27}}[/tex]
point is (27, 0)
• Considering the second line: y = mx + b
[tex]\dashrightarrow \: { \tt{0 = (3 \times 27) + b}} \\ \\ { \tt{b = - 81}}[/tex]
