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 the slope $m$

The slope - formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's assume two points on the line: $(x_1,y_1)=(0,2)$ and $(x_2,y_2)=(2,3)$. Then $m=\frac{3 - 2}{2 - 0}=\frac{1}{2}$.

Step2: Find the y - intercept $b$

The y - intercept is the y - value when $x = 0$. From the point $(0,2)$, we know that $b = 2$.

Step3: Write the equation of the line

The slope - intercept form of a line is $y=mx + b$. Substituting $m=\frac{1}{2}$ and $b = 2$ into the formula, we get $y=\frac{1}{2}x+2$.

Answer:

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