Question

write the equation of this line in slope - intercept form.

Explanation:

Step1: Identify slope-intercept form

Slope - intercept form 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 $(0,1)$, so $b = 1$.

Step3: Calculate the slope ($m$)

We can use two points on the line. Let's take $(0,1)$ and $(1,5)$ (we can see from the graph that when $x = 1$, $y = 5$). The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$.
Substituting $x_1 = 0,y_1 = 1,x_2 = 1,y_2 = 5$ into the formula: $m=\frac{5 - 1}{1 - 0}=\frac{4}{1}=4$.

Step4: Write the equation

Substitute $m = 4$ and $b = 1$ into $y=mx + b$. We get $y = 4x+1$.

Answer:

$y = 4x + 1$