Question

Can you pls. Help me how to solve this?

Answer 1

y = -
`(1)/(2)` x -
`(5)/(2)`

Explanation:

the equation of a line in slope- intercept form is

y = mx + b ( m is the slope and b the y-intercept )

y = 2x - 3 is in this form with slope m = 2

given a line with slope m , then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(2)`

y = -
`(1)/(2)` x + b ← is the partial equation

too find b substitute (1, - 3) into the partial equation

- 3 = -
`(1)/(2)` + b ⇒ b = - 3 +
`(1)/(2)` = -
`(5)/(2)`

y = -
`(1)/(2)` x -
`(5)/(2)` ← equation of line

Answer 2

Answer:
`\bold{y=-(1)/(2)x-(5)/(2)}`

Explanation:

perpendicular to y = 2x - 3
`\rightarrow m=2\qquad m\perp =-(1)/(2)`

Input the slope
`\bigg(m_\perp=-(1)/(2)\bigg)` and the point (x₁, y₁) = (1, -3) into the Point-Slope formula: y - y₁ = m(x - x₁)

`y - (-3)=-(1)/(2)(x - 1)\\\\y + 3 = -(1)/(2)x + (1)/(2)\\\\y = -(1)/(2)x -(5)/(2)\\`