write the equation of this line in slope-intercept form.\nwrite your answer using integers, proper…

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 $(0,14)$. So, $b = 14$.

Step3: Calculate the slope ($m$)

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points on the line. We know the y - intercept is $(0,14)$ and we can take another point, for example, when $x=- 6$, $y = 10$ (from the graph: when $x=-6$, the line passes through $y = 10$). So, let $(x_1,y_1)=(0,14)$ and $(x_2,y_2)=(-6,10)$. Then $m=\frac{10 - 14}{-6-0}=\frac{-4}{-6}=\frac{2}{3}$. We can also check with another pair of points. Let's take $(x_1,y_1)=(0,14)$ and $(x_2,y_2)=(3,16)$. Then $m=\frac{16 - 14}{3 - 0}=\frac{2}{3}$.

Step4: Write the equation

Substitute $m=\frac{2}{3}$ and $b = 14$ into the slope - intercept form $y=mx + b$. We get $y=\frac{2}{3}x+14$.

Answer:

$y=\frac{2}{3}x + 14$