Question

write an equation for the line shown on the right.

the equation of the line is \\(\square\\).
(type an equation. type your answer in slope - intercept form. use integers or simplified fractions for any numbers in the expression.)

Explanation:

Step1: Identify y-intercept

The line crosses the y-axis at $(0, 6)$, so $b=6$.

Step2: Calculate slope

Use two points $(0,6)$ and $(3,9)$. Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{9-6}{3-0}=\frac{3}{3}=1$

Step3: Write slope-intercept form

Slope-intercept form: $y=mx+b$
Substitute $m=1$, $b=6$: $y=1x+6$

Answer:

$y=x+6$