Question

5.5 graphing lines with slope and y - intercept write an equation in slope - intercept form, y = mx + b, for the graph below. be sure to put a space between symbols.

Explanation:

Step1: Identify y - intercept

The line crosses the y - axis at $y = 5$, so $b = 5$.

Step2: Calculate slope

Using two points $(0,5)$ and $(1,3)$. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1 = 0,y_1 = 5,x_2 = 1,y_2 = 3$. Then $m=\frac{3 - 5}{1-0}=\frac{- 2}{1}=-2$.

Step3: Write the equation

Substitute $m=-2$ and $b = 5$ into $y=mx + b$. We get $y=-2x + 5$.

Answer:

$y=-2x + 5$