Determine the equation of a line given its slope and $y$-intercept. Write in slope-intercept form.
Slope = $-3$
$y$-intercept = $\frac{5}{2}$

• A. $y=-3x+\(\frac\)52$
• B. $y=\(\frac\)52x-3$
• C. $y=\(\frac\)52x+3$
• D. $y=3x-\(\frac\)52$

Answer: (A)

Verified step by step guidance

1. Recall the slope-intercept form of a line, which is given by the equation \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
2. Identify the given slope \(m\) and y-intercept \(b\) from the problem. Here, the slope \(m = -3\) and the y-intercept \(b = \frac{5}{2}\).
3. Substitute the given slope and y-intercept values into the slope-intercept form equation: \(y = (-3)x + \frac{5}{2}\).
4. Simplify the equation if necessary, but in this case, the equation is already in its simplest slope-intercept form.
5. Write the final equation of the line as \(y = -3x + \frac{5}{2}\), which expresses the line with the given slope and y-intercept.