Question

4. Which line is perpendicular to y = 7*-3 if the perpendicular line passes through the point (7, 7)?

Oy=-x+8
y=-7x+8
Oy=-7x+1
Oy=-x+1

Answer 1

The correct option is (a) that is

`\large \bf\implies{y = - (1)/(7)x + 8}`

Step-by-step explanation :

Step 1) : Find the slope of the line is perpendicular to y = 7x - 3 :

`\bf \longrightarrow{m = - (1)/(7) }`

Step 2) : Substitute and Calculate :

`Substitute \begin{cases}m = - (1)/(7) & \text{} \\x = 7& \text{into \: y = mx + b} \\ y = 1& \text{}\end{cases}`

Putting the values according to the formula (y = mx + b)

`\bf \longrightarrow{7 = - (1)/(7) * 7 + b}`

Calculate it

`\bf \Longrightarrow{7 = - \frac{1}{ \cancel{7}} * \cancel{7} + b} \\ \\ \bf \Longrightarrow{7 = - 1 + b} \\ \\ \bf \Longrightarrow{7 + 1 = b} \\ \\ \bf \Longrightarrow{8 = b} \\ \\ \bf{\therefore{b = 8}}`

`Substitute \begin{cases}m = - (1)/(7) & \text{} \\& \text{into \: y = mx + b} \\ b = 8& \text{}\end{cases}`

`\huge \mapsto\boxed{ \red{y = - (1)/(7)x + 8}}`

Hence, the correct option is (a).