Respuesta :

Answer:

[tex]y=\frac{1}{3}x[/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 the line passes through are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in the given points (-3,-1) and (6,2)

[tex]=\frac{2-(-1)}{6-(-3)}\\=\frac{2+1}{6+3}\\=\frac{3}{9}\\=\frac{1}{3}[/tex]

Therefore, the slope of the line is [tex]\frac{1}{3}[/tex]. Plug this into [tex]y=mx+b[/tex]:

[tex]y=\frac{1}{3}x+b[/tex]

2) Determine the y-intercept (b)

[tex]y=\frac{1}{3}x+b[/tex]

Plug in one of the given points and solve for b

[tex]2=\frac{1}{3}(6)+b\\2=2+b[/tex]

Subtract 2 from both sides to isolate b

[tex]2-2=2+b-2\\0=b[/tex]

Therefore, the y-intercept is equal to 0. Plug this back into [tex]y=\frac{1}{3}x+b[/tex]:

[tex]y=\frac{1}{3}x+0\\y=\frac{1}{3}x[/tex]

I hope this helps!

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