Mathematics: The lines given by the equation y = 9 - 1/3x and y = mx + b are perpendicular and intersect at a point on the x axis. What is the value of b?

He hit the slopes I think This is the answer but I’m not sure...

The lines given by the equation y = 9 - 1/3x and

poohmoney

18.09.2021

• Since these lines are perpendicular, their product of their gradients is negative one:

$\dashrightarrow \: { \tt{m_{1} \times m _{2} = - 1 }}$

• m1 is gradient of first line.

• m2 is gradient of second line.

$\dashrightarrow \: { \tt{ - \frac{1}{3} \times m_{2} = - 1}} \\ \\ \hookrightarrow \: { \underline{ \tt{ \: \: m _{2} = 3 \: \: }}}$

• since they intersect at a point on x-axis, y = 0

• Considering the first line: y = 9 - ⅓x

$\dashrightarrow \: { \tt{0 = 9 - \frac{1}{3} x}} \\ \\ { \tt{x = 9 \times 3 = 27}}$

point is (27, 0)

• Considering the second line: y = mx + b

$\dashrightarrow \: { \tt{0 = (3 \times 27) + b}} \\ \\ { \tt{b = - 81}}$

0,0(0 оценок)