Respuesta :

Answer:

A

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 )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, - 2.5) and (x₂, y₂ ) = (2, 1) ← 2 points on the line

m = [tex]\frac{1+2.5}{2-0}[/tex] = [tex]\frac{3.5}{2}[/tex] = [tex]\frac{7}{4}[/tex]

Note the line crosses the y- axis at (0, - 2.5) ⇒ c = - 2.5 = - [tex]\frac{5}{2}[/tex]

y =  [tex]\frac{7}{4}[/tex] x - [tex]\frac{5}{2}[/tex] → A

JeanaShupp

Answer:  [tex]y=\dfrac{7}{4}x-\dfrac{5}{2}[/tex]

Step-by-step explanation:

The equation of a line passing through points (a,b) and (c,d) is given by :-

[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]

From the given graph , it can be seen that the line is passing through (0,-2.5) and (2,1).

Then, the equation of line passing through (0,-2.5) and (2,1) will be:-

[tex](y-1)=\dfrac{1-(-2.5)}{2-0}(x-2)\\\\\Rightarrow\ (y-1)=\dfrac{1+2.5}{2}(x-2)\\\\\Rightarrow\ y-1=\dfrac{3.5}{2}(x-2)\\\\\Rightarrow\ y-1=\dfrac{7}{4}(x-2) \ \ [\because 3.5=\dfrac{7}{2}]\\\\\Rightarrow\ y-1=\dfrac{7}{4}x-\dfrac{7}{4}\times2\\\\\Rightarrow\ y=\dfrac{7}{4}x-\dfrac{7}{2}+1\\\\\Rightarrow\ y=\dfrac{7}{4}x+\dfrac{-7+2}{2}\\\\\Rightarrow\ y=\dfrac{7}{4}x-\dfrac{5}{2}[/tex]

Hence, the equation of the graph is [tex]y=\dfrac{7}{4}x-\dfrac{5}{2}[/tex]

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