Question

The line L3 is perpendicular to 3x-y+2=0 .find the gradient of L3

Answer 1

`-(1)/(3)`

Step-by-step explanation:

Here, we want to get the gradient of the line L3

The equation of a straight line can be expressed as:

`y\text{ = mx + b}`

where m is the gradient (slope) and b is the y-intercept (the y-value when x = 0)

Now,let us write the equation of the first line in the slope-intercept form

Mathematically, we have this as:

`\begin{gathered} 3x-y\text{ + 2 = 0} \\ y\text{ = 3x + 2} \end{gathered}`

The gradient of the first line is 3

Now,let us get the gradient of the second line L3

Mathematically, when two lines ae perpendicular, the product of their gradients (slopes) equal -1

Thus, we have it that:

`\begin{gathered} m_1\text{ }* m_2\text{ = -1} \\ 3\text{ }* m_2\text{ = -1} \\ m_2\text{ = -}(1)/(3) \end{gathered}`