Question

write an equation for the line shown on the right. the equation of the line is y = . (type an expression using x as the variable. simplify your answer. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Find two points on the line

Let's take two points from the graph, say $(0, 3)$ and $(6, 6)$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting $(x_1,y_1)=(0,3)$ and $(x_2,y_2)=(6,6)$ gives $m=\frac{6 - 3}{6 - 0}=\frac{3}{6}=\frac{1}{2}$.

Step3: Use the slope - intercept form $y=mx + b$

We know that when $x = 0$, $y=3$, so the $y$-intercept $b = 3$.

Step4: Write the equation of the line

Substituting $m=\frac{1}{2}$ and $b = 3$ into $y=mx + b$, we get $y=\frac{1}{2}x+3$.

Answer:

$y=\frac{1}{2}x + 3$