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Write an equation of the line that passes through the points (3.2) and (6,11). Show your work!

Sagot :

theleangreenbean

Answer:

[tex]y=3x-7[/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 the points given are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Points (3,2) and (6,11)

[tex]=\frac{11-2}{6-3}\\=\frac{9}{3}\\= 3[/tex]

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

[tex]y=3x+b[/tex]

2) Determine the y-intercept (b)

[tex]y=3x+b[/tex]

Plug in one of the given points and solve for b

[tex]2=3(3)+b\\2=9+b[/tex]

Subtract 9 from both sides

[tex]2-9=9+b-9\\-7=b[/tex]

Therefore, the y-intercept of the line is -7. Plug this back into [tex]y=3x+b[/tex]:

[tex]y=3x-7[/tex]

I hope this helps!

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