Question

Can someone answer this, please?

Answer 1

`\sf y =(2)/(5)x-4`

Explanation:

Slope intercept form:

To find the equation of the required line, first we need to find the slope of the given line in the graph.

Choose two points from the graph.

(0 ,4) x₁ = 0 & y₁ = 4

(2,-1) x₂ = 2 & y₂ = -1

`\sf \boxed{\sf \bf Slope=(y_2-y_1)/(x_2-x_1)}`

`\sf = (-1-4)/(2-0)\\\\=(-5)/(2)`

`\sf m_1=(-5)/(2)`

`\sf \text{Slope of the perpendicular line m = $(-1)/(m_1)$}`

`\sf = -1 / (-5)/(2)\\\\=-1 * (-2)/(5)\\\\=(2)/(5)`

`\boxed{\sf slope \ intercept \ form \ : \ y = mx + b}`

Here, m is slope and b is y-intercept.

Substitute the m value in the above equation,

`\sf y =(2)/(5)x + b`

The line is passing through (5 , -2),

`\sf -2 = (2)/(5)*5+b`

-2 = 2 + b

-2 - 2 = b

b = -4

Slope-intercept form:

`\sf y = (2)/(5)x-4`