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 $(0,6)$, so $b = 6$.

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 $(0,6)$ and the x - intercept $(- 6,0)$.
Substitute $x_1 = 0,y_1 = 6,x_2=-6,y_2 = 0$ into the slope formula:
$m=\frac{0 - 6}{-6-0}=\frac{-6}{-6}=1$

Step4: Write the equation

Substitute $m = 1$ and $b = 6$ into the slope - intercept form $y=mx + b$.
We get $y=x + 6$.

Answer:

$y = x+6$