Question

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

Explanation:

Step1: Identify 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

The line crosses the y - axis at the point $(0,2)$, so $b = 2$.

Step3: Find the slope

Using two points on the line, say $(0,2)$ and $(3,4)$. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1 = 0,y_1 = 2,x_2=3,y_2 = 4$. Then $m=\frac{4 - 2}{3 - 0}=\frac{2}{3}$.

Step4: Write the equation

Substitute $m=\frac{2}{3}$ and $b = 2$ into $y=mx + b$. We get $y=\frac{2}{3}x+2$.

Answer:

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