Write an equation in slope-intercept form for the line with slope $-\frac{1}{3}$ and $y$-intercept 5 . Then graph the line.
Equation:
Answer
The equation of the line in slope-intercept form is \(\boxed{y = -\frac{1}{3}x + 5}\).
Step 1 ：The slope-intercept form of a line is given by \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
Step 2 ：Substitute \(m = -\frac{1}{3}\) and \(b = 5\) into the equation to get \(y = -\frac{1}{3}x + 5\).
Step 3 ：To graph the line, start by plotting the y-intercept at (0,5).
Step 4 ：Since the slope is -\frac{1}{3}, from the point (0,5), move down 1 unit and to the right 3 units to find another point on the line.
Step 5 ：Draw a line through these two points to graph the line.
Step 6 ：The equation of the line in slope-intercept form is \(\boxed{y = -\frac{1}{3}x + 5}\).
