Questions: Equation: and then state the y-intercept. 12. (0,-20) and (6,-2) a. Slope: b. Y-intercept:

Transcript text: Equation: $\qquad$ and then state the $y$-intercept. 12. $(0,-20)$ and $(6,-2)$ a. Slope: $\qquad$ b. Y-intercept: $\qquad$

Solution

Solution Steps

To find the slope and y-intercept of the line passing through the points (0, -20) and (6, -2), we can use the following steps:

Calculate the slope using the formula: $ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} $.
Use the slope and one of the points to find the y-intercept using the equation of a line: $ y = mx + b $.

Step 1: Calculate the Slope

To find the slope $ m $ of the line passing through the points $ (0, -20) $ and $ (6, -2) $, we use the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - (-20)}{6 - 0} = \frac{18}{6} = 3.0 \]

Step 2: Calculate the Y-Intercept

Using the slope $ m = 3.0 $ and the point $ (0, -20) $, we can find the y-intercept $ b $ using the equation of the line: \[ y = mx + b \implies -20 = 3.0 \cdot 0 + b \implies b = -20.0 \]