Answered

Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Our platform provides a seamless experience for finding precise answers from a network of experienced professionals. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

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!

Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.