Respuesta :

4)

If you know the slope [tex]m[/tex] and a point [tex](x_0,y_0)[/tex] belonging to a line, then the equation of the line is

[tex]y-y_0=m(x-x_0)[/tex]

In your case, you have [tex]m=-\frac{1}{2}[/tex] and [tex](x_0,y_0)=(6,5)[/tex]. So, the equation of the line is

[tex]y-5=-\dfrac{1}{2}(x-6) \iff y = -\dfrac{1}{2}x+8[/tex]

5)

If you know two points [tex](x_1,y_1),\ (x_2,y_2)[/tex] belonging to a line, then the equation of the line is

[tex]\dfrac{y-y_2}{y_1-y_2}=\dfrac{x-x_2}{x_1-x_2}[/tex]

In your case, you have [tex](x_1,y_1)=(-2,3)[/tex] and [tex](x_2,y_2)=(2,5)[/tex]. So, the equation of the line is

[tex]\dfrac{y-5}{3-5}=\dfrac{x-2}{-2-2} \iff \dfrac{y-5}{-8}=\dfrac{x-2}{-4} \iff y-5 = 2x-4 \iff y = 2x+1[/tex]

tramserran

Answer:  [tex]\bold{4)\quad y=-\dfrac{1}{2}x+8}[/tex]

                [tex]\bold{5)\quad y=\dfrac{1}{2}x+4}[/tex]

Step-by-step explanation:

Use the Point-Slope formula: y - y₁ = m(x - x₁)   where

  • (x₁ , y₁) is a point
  • m is the slope

[tex]y-5=-\dfrac{1}{2}(x-6)\\\\\\y-5=-\dfrac{1}{2}x+3\\\\\\.\quad \large\boxed{y=-\dfrac{1}{2}x+8}[/tex]

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Find the slope using the formula: [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Then use the Point-Slope formula using ONE of the points as (x₁ , y₁)

[tex]m=\dfrac{5-3}{2-(-2)}=\dfrac{2}{4}=\boxed{\dfrac{1}{2}}[/tex]

[tex]y-5=\dfrac{1}{2}(x-2)\\\\\\y-5=\dfrac{1}{2}x-1\\\\\\.\quad \large\boxed{y=\dfrac{1}{2}x+4}[/tex]

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