197k views
22 votes
A line passes through ( – 8,6) and ( – 2, 3).
Find the y-intercept, b, of the line.

User Portable
by
8.4k points

1 Answer

13 votes

Answer:


\displaystyle [0, 2]

Step-by-step Step-by-step explanation:

First, find the rate of change [slopes]:


\displaystyle (-y_1 + y_2)/(-x_1 + x_2) = m \\ \\ (-6 + 3)/(8 - 2) = m; (-3)/(6) \\ \\ -(1)/(2) = m

We now plug the above information into the Slope-Intercept Formula. It does not matter which ordered pair is selected:


\displaystyle y = mx + b \\ \\ 3 = -(1)/(2)[-2] + b \hookrightarrow 3 = 1 + b; \boxed{2 = b} \\ \\ y = -(1)/(2)x + 2

OR


\displaystyle y = mx + b \\ \\ 6 = -(1)/(2)[-8] + b \hookrightarrow 6 = 4 + b; \boxed{2 = b} \\ \\ y = -(1)/(2)x + 2

Therefore, the line passes through the y-intercept of
\displaystyle [0, 2].

I am joyous to assist you at any time.

User Jbellis
by
7.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories