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 line crosses the y - axis at $(0,7)$, so $b = 7$.

Step3: Calculate the slope ($m$)

We can use two points on the line. Let's take $(0,7)$ and $(8,8)$ (we can see that when $x$ increases by 8, $y$ increases by 1). The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting $(x_1,y_1)=(0,7)$ and $(x_2,y_2)=(8,8)$, we get $m=\frac{8 - 7}{8 - 0}=\frac{1}{8}$.

Step4: Write the equation

Substitute $m=\frac{1}{8}$ and $b = 7$ into the slope - intercept form $y=mx + b$. So the equation is $y=\frac{1}{8}x + 7$.

Answer:

$y=\frac{1}{8}x + 7$