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 $(0,2)$, so $b = 2$.

Step3: Calculate the slope ($m$)

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

Step4: Write the equation in slope - intercept form

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

Answer:

$y = 2x+2$