Respuesta :

Answer:

y = - [tex]\frac{1}{2}[/tex] x - [tex]\frac{5}{2}[/tex]

Step-by-step 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

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex]

y = - [tex]\frac{1}{2}[/tex] x + b ← is the partial equation

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

- 3 = - [tex]\frac{1}{2}[/tex] + b ⇒ b = - 3 + [tex]\frac{1}{2}[/tex] = - [tex]\frac{5}{2}[/tex]

y = - [tex]\frac{1}{2}[/tex] x - [tex]\frac{5}{2}[/tex] ← equation of line


tramserran

Answer: [tex]\bold{y=-\dfrac{1}{2}x-\dfrac{5}{2}}[/tex]

Step-by-step explanation:

perpendicular to y = 2x - 3   [tex]\rightarrow m=2\qquad m\perp =-\dfrac{1}{2}[/tex]

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

[tex]y - (-3)=-\dfrac{1}{2}(x - 1)\\\\y + 3 = -\dfrac{1}{2}x + \dfrac{1}{2}\\\\y = -\dfrac{1}{2}x -\dfrac{5}{2}\\[/tex]

Otras preguntas