write an equation of the line that passes through the pair of points. (0, 1), (5, 3)

Explanation:

Step1: Find the slope

The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(0,1)$ and $(x_2,y_2)=(5,3)$. Then $m=\frac{3 - 1}{5 - 0}=\frac{2}{5}$.

Step2: Use the 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. We know $m=\frac{2}{5}$, and since the line passes through $(0,1)$, when $x = 0$, $y=1$, so $b = 1$.

Step3: Write the equation

Substitute $m=\frac{2}{5}$ and $b = 1$ into $y=mx + b$, we get $y=\frac{2}{5}x+1$.

Answer:

$y=\frac{2}{5}x + 1$