y = 1/3x + 5
Understand the Problem
The question provides a linear equation in slope-intercept form, which is asking about the relationship between the variables x and y. Typically, the goal would be to analyze this equation further, such as finding the slope and y-intercept, or graphing it.
Answer
The slope $m$ and y-intercept $b$ need to be identified from the linear equation for analysis, $y = mx + b$.
Answer for screen readers
The answer will vary depending on the specific equation provided. However, the identified slope ($m$) and y-intercept ($b$) will guide you, and you can use specific $x$ values to calculate respective $y$ values.
Steps to Solve
- Identify the Slope and Y-Intercept
In slope-intercept form, a linear equation is expressed as $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. Identify these values from the given equation.
- Substituting Values
If you are required to find a specific value such as $y$ for a given $x$, substitute the value of $x$ into the equation. For example, if the equation is $y = 2x + 3$ and you need to find $y$ when $x = 4$, substitute 4 for $x$:
$$ y = 2(4) + 3 $$
- Calculate the Result
Perform the arithmetic operations to find $y$. Continuing from the previous example:
$$ y = 8 + 3 = 11 $$
- Graphing the Equation (if required)
If asked to graph it, plot the y-intercept $(0, b)$ on the y-axis and use the slope $m$ (rise over run) to determine another point. For example, with a slope of 2 (which is $2/1$), from the intercept point, go up 2 units and right 1 unit to find another point.
- Draw the Line
Finally, draw a line through the points you've plotted to represent the linear equation graphically.
The answer will vary depending on the specific equation provided. However, the identified slope ($m$) and y-intercept ($b$) will guide you, and you can use specific $x$ values to calculate respective $y$ values.
More Information
The slope ($m$) shows how steep the line is, while the y-intercept ($b$) indicates where the line crosses the y-axis. Understanding these components is crucial for interpreting linear relationships in real-world contexts.
Tips
- Misinterpreting the slope or y-intercept values.
- Forgetting to perform arithmetic correctly when substituting values.
- Confusing positive and negative slopes when graphing.
