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The point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is y – 4 = (x – 8). What is the slope-intercept form of the equation for this line?

A) y = 1/4x – 12
B) y = 1/4x – 4
C) y = 1/4x + 2
D) y = 1/4 x + 6

Respuesta :

dalendrk
[tex]y-4=\dfrac{1}{4}(x-8)[/tex]

The slope-intercept form: [tex]y=mx+b[/tex]

m - a slope
b - y-intercept (0; b)

The point-slope form: [tex]y-y_0=m(x-x_0)[/tex]

therefore [tex]m=\dfrac{1}{4}[/tex]

We have a point (0; 2) ⇒ it's the y-intercept, therefore [tex]b=2[/tex]


Answer: [tex]C)\ y=\dfrac{1}{4}x+2[/tex]

Other method:

[tex]y-4=\dfrac{1}{4}(x-8)\ \ \ \ \ |use\ distributive\ property:\ a(b-c)=ab-ac\\\\y-4=\dfrac{1}{4}x-2\ \ \ \ \ \ |add\ 4\ to\ both\ sides\\\\y=\dfrac{1}{4}x+2[/tex]

Answer:c

Step-by-step explanation:

bc