The problem asks us to find the slope and y-intercept of a given line, and then write the equation of the line in slope-intercept form ($y = mx + b$). We are given that the y-intercept is at $(0,1)$ and the slope of the line is $\frac{5}{2}$.

1. Problem Description

The problem asks us to find the slope and y-intercept of a given line, and then write the equation of the line in slope-intercept form ($y = mx + b$). We are given that the y-intercept is at $(0,1)$ and the slope of the line is $\frac{5}{2}$.

2. Solution Steps

The slope-intercept form of a line is given by:

$y = mx + b$

where $m$ is the slope and $b$ is the y-intercept.

We are given that the y-intercept is $(0, 1)$, so $b = 1$.

We are also given that the slope is $m = \frac{5}{2}$.

Substituting these values into the slope-intercept form, we get:

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

3. Final Answer

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