Respuesta :

Answer:

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

Step-by-step explanation:

the equation of a line in slope- intercept form is

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

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

the point (0, 1 ) is the y- intercept ⇒ c = 1

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

This is about equation of a straight line in slope intercept form.

Equation of the straight line is y = [tex]\frac{1}{2}x + 1[/tex]

  • Formula for equation of line in slope intercept form is;

y = mx + c

where m is slope and c is y-intercept

  • We are given;

A line passing through the point (0, 1)

This line is perpendicular to the line y = -2x + 2

  • Comparing y = -2x + 2 to y = mx + c, we can say that;

m = -2

  • Now, for line perpendicular to this one with slope of m = -2, that line will have a slope of; m' = -1/m

Thus, slope of new line = -1/-2 = 1/2

  • Equation of that straight line would be gotten from;

y - y1 = m(x - x1)

This gives;

y - 1 = (1/2)(x - 0)

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

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

Read more at; https://brainly.com/question/12703665

Otras preguntas