Respuesta :

kudzordzifrancis

Answer:

D. [tex]x+4y=12[/tex]

Step-by-step explanation:

The given equation passes through:

(4,2) and (8,1).

The equation can be obtained using the formula;

[tex]y-y_1=m(x-x_1)[/tex]

The slope is given by:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Let [tex](x_1,y_1)=(4,2)[/tex] and  [tex](x_2,y_2)=(8,1)[/tex], then we have;

[tex]m=\frac{1-2}{8-4} =-\frac{1}{4}[/tex]

we now plug in the slope and the point to obtain;

[tex]y-2=-\frac{1}{4}(x-4)[/tex]

We multiply through by 4 to obtain;

[tex]4(y-2)=-(x-4)[/tex]

Expand using the distributive property;

[tex]4y-8=-x+4[/tex]

[tex]4y+x=4+8[/tex]

[tex]x+4y=12[/tex]

luisejr77

Answer: Option D.

Step-by-step explanation:

The Standard form of the equation of then line is:

[tex]Ax+By=C[/tex]

Where A, B and C are integers.

The Point-slope form of the equationof the line is:

[tex]y-y_1=m(x-x_1)[/tex]

Where m is the slope of the line and ([tex]x_1,y_1[/tex]) is a point of the line.

Given the points (4,2) and (8,1), you can find the slope with the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]. Then:

[tex]m=\frac{1-2}{8-4}=-\frac{1}{4}[/tex]

Substitute the slope and the point (4,2 ) into [tex]y-y_1=m(x-x_1)[/tex]:

[tex]y-2=-\frac{1}{4}(x-4)[/tex]

To write in Standard form, move the variables to one sides of the equation. Then:

[tex]y-2=-\frac{1}{4}(x-4)\\\\4(y-2)=x-4\\4y-8=-x+4\\x+4y=4+8\\x+4y=12[/tex]

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