Question

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

Answer 1

Answer:

$\displaystyle [0, 2]$

Step-by-step explanation:

First, find the rate of change [slopes]:

$\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{-6 + 3}{8 - 2} = m; \frac{-3}{6} \\ \\ -\frac{1}{2} = m$

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

$\displaystyle y = mx + b \\ \\ 3 = -\frac{1}{2}[-2] + b \hookrightarrow 3 = 1 + b; \boxed{2 = b} \\ \\ y = -\frac{1}{2}x + 2$

OR

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

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

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