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. $y=-3x+\frac{5}{2}$
• B. $y=\frac{5}{2}x-3$
• C. $y=\frac{5}{2}x+3$
• D. $y=3x-\frac{5}{2}$

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 slope \(m\) from the problem. Here, the slope is given as \(-3\).
3. Identify the y-intercept \(b\) from the problem. Here, the y-intercept is given as \(\frac{5}{2}\).
4. Substitute the slope \(m = -3\) and the y-intercept \(b = \frac{5}{2}\) into the slope-intercept form equation to get \(y = -3x + \frac{5}{2}\).
5. This equation represents the line with the given slope and y-intercept in slope-intercept form.