Question

Write and equation in slope intercept form for the line that is perpendicular to the line you graphed using y=-5/2x-3 and passing through points (-5,2)

Answer 1

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

Explanation:

`\sf y = (-5)/(2)x-3\\\\\\m_1=(-5)/(2)`

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

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

`\sf slope = m = (2)/(5)`

Line passes thorugh ( -5 , 2)

Equation of line: y = mx + b

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

Substitute the point(-5,2) in the above equation and find the value of 'b'.

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

2+ 2 = b

b = 4

Equation of the line :

`\sf \boxed{y =(2)/(5)x+4}`