Question

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

Answer 1

`\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].`

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