Question

write the equation of this line in slope-intercept form.
write your answer using integers, proper fractions, and improper fractions in simplest 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 line crosses the y - axis at $(0,14)$, so $b = 14$.

Step3: Calculate the slope ($m$)

We can use two points on the line. Let's take $(0,14)$ and $(- 7,7)$ (we can find another point by moving left 7 units and down 7 units from $(0,14)$). The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Using $(x_1,y_1)=(0,14)$ and $(x_2,y_2)=(-7,7)$, we have $m=\frac{7 - 14}{-7-0}=\frac{-7}{-7} = 1$. We can also check with another pair of points. For example, from $(0,14)$ to $(2,16)$, $m=\frac{16 - 14}{2-0}=\frac{2}{2}=1$.

Step4: Write the equation

Substitute $m = 1$ and $b = 14$ into the slope - intercept form $y=mx + b$. We get $y=x + 14$.

Answer:

$y = x+14$