Question

write the equation of this line in slope - intercept form.

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Find the y - intercept ($b$)

The y - intercept is the point where the line crosses the y - axis. From the graph, the line crosses the y - axis at $(0, - 3)$, so $b=-3$.

Step3: Calculate the slope ($m$)

We can use two points on the line to find the slope. Let's use the y - intercept $(0, - 3)$ and another point, say $(2,1)$ (we can see from the graph that when $x = 2$, $y = 1$). The formula for slope is $m=\frac{y_2 - y_1}{x_2 - x_1}$.
Substituting $x_1 = 0,y_1=-3,x_2 = 2,y_2 = 1$ into the formula:
$m=\frac{1-(-3)}{2 - 0}=\frac{1 + 3}{2}=\frac{4}{2}=2$

Step4: Write the equation

Now that we have $m = 2$ and $b=-3$, substitute these values into the slope - intercept form $y=mx + b$.
We get $y = 2x-3$.

Answer:

$y = 2x-3$