Question

5.5 graphing lines with slope and y - intercept
looking at the graphs below, identify the slope and the y - intercept.
1 m = b =
2 m = b =

Explanation:

Step1: Recall slope formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For the first graph, we can use the points $(0,5)$ and $(3,3)$.

Step2: Calculate slope of first graph

$m_1=\frac{3 - 5}{3-0}=\frac{-2}{3}=-\frac{2}{3}$. The y - intercept is the y - value when $x = 0$, so $b_1 = 5$.

Step3: For second graph, assume two points

Let's assume two points on the second graph, say $(0,-3)$ (the y - intercept) and $(3, - 2)$.

Step4: Calculate slope of second graph

$m_2=\frac{-2-(-3)}{3 - 0}=\frac{-2 + 3}{3}=\frac{1}{3}$. The y - intercept $b_2=-3$.

Answer:

1. $m=-\frac{2}{3}$, $b = 5$
2. $m=\frac{1}{3}$, $b=-3$