Question

18a. write a rule (equation) for the graph below. *

Explanation:

Step1: Identify slope-intercept form

The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. From the graph, we can see that the line crosses the y - axis at $(0,3)$, so $b = 3$.

Step2: Calculate the slope

To find the slope $m$, we can use two points on the line. We know one point is $(0,3)$ and another point can be found from the graph. Let's take the point $(1,1)$ (we can also use other points). The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(0,3)$ and $(x_2,y_2)=(1,1)$. Then $m=\frac{1 - 3}{1 - 0}=\frac{- 2}{1}=-2$. We can also check with another point, say when $x = 0$, $y = 3$ and when $x = 1$, $y = 1$, the change in $y$ is $1 - 3=-2$ and change in $x$ is $1 - 0 = 1$, so slope $m=-2$.

Step3: Write the equation

Substitute $m=-2$ and $b = 3$ into the slope - intercept form $y=mx + b$. We get $y=-2x + 3$.

Answer:

$y=-2x + 3$