Respuesta :

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

the equation of a line in slope-intercept form is

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

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 2 ) and (x₂, y₂ ) = (- 4, 0 ) ← points from graph

m = [tex]\frac{0-2}{-4-0}[/tex] = [tex]\frac{-2}{-4}[/tex] = [tex]\frac{1}{2}[/tex]

from the graph the y-intercept = (0, 2 ) → c = 2

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

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

  • The calculation is as follows:

The equation of a line in slope-intercept form is

y = mx + c

Here m is the slope and c is the y-intercept  

 

Now  

[tex]m = ( y_2 - y_1 ) \div (x_2 - x_1 )[/tex]

Here

[tex](x_1, y_1 )[/tex]= (0, 2 ) and [tex](x_2, y_2 )[/tex] = (- 4, 0 )  

Now  

[tex]m = (0-2) \div (-4-0)\\\\= -2\div -4\\\\= \frac{1}{2}[/tex]

From the graph the y-intercept = (0, 2 ) i.e. c = 2

Learn more; brainly.com/question/17429689

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