Respuesta :

Answer:

[tex]y=\frac{1}{2}x-6[/tex]

Step-by-step explanation:

Hi there!

Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)

1) Determine the slope (m)

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] where two points that fall on the line are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in the given points (2,-5) and (8,-2)

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\=\frac{-2-(-5)}{8-2}\\=\frac{-2+5}{8-2}\\=\frac{3}{6}\\=\frac{1}{2}[/tex]

Therefore, the slope of the line is [tex]\frac{1}{2}[/tex]. Plug this into [tex]y=mx+b[/tex]:

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

2) Determine the y-intercept (b)

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

Plug in one of the given points and solve for b

[tex]-5=\frac{1}{2}(2)+b\\-5=1+b[/tex]

Subtract 1 from both sides to isolate b

[tex]-5-1=1+b-1\\-6=b[/tex]

Therefore, the y-intercept of the line is -6. Plug this back into [tex]y=\frac{1}{2}x+b[/tex]:

[tex]y=\frac{1}{2}x+(-6)\\y=\frac{1}{2}x-6[/tex]

I hope this helps!

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