Questions: Plot the linear function using its slope and y-intercept f(x)=1/3 x-1

Transcript text: Plot the linear function using its slope and $y$-intercept \[ f(x)=\frac{1}{3} x-1 \]

Solution

Solution Steps

Step 1: Identify the Slope and Y-intercept

The given linear function is $ f(x) = \frac{1}{3}x - 1 $. Here, the slope $ m $ is $ \frac{1}{3} $ and the y-intercept $ b $ is $-1$.

Step 2: Determine the Equation of the Line

The equation of the line is already given as $ f(x) = \frac{1}{3}x - 1 $.

Step 3: Calculate Key Points

To plot the line, we can calculate a couple of key points. For example:

When $ x = 0 $, $ f(0) = \frac{1}{3}(0) - 1 = -1 $.
When $ x = 3 $, $ f(3) = \frac{1}{3}(3) - 1 = 0 $.

Final Answer

The linear function $ f(x) = \frac{1}{3}x - 1 $ has a slope of $ \frac{1}{3} $ and a y-intercept of $-1$. Key points for plotting include (0, -1) and (3, 0).

{"axisType": 3, "coordSystem": {"xmin": -5, "xmax": 5, "ymin": -5, "ymax": 5}, "commands": ["y = (1/3)x - 1"], "latex_expressions": ["$y = \\frac{1}{3}x - 1$"]}

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!