Find the slope and y-intercept of the line 3x+y=4. Then use them to graph the line.
Understand the Problem
The question provides the equation of a line in the form 3x+y=4. It asks you to find the slope and y-intercept of the line, and then use those parameters to graph the line.
Answer
Slope: $-3$ Y-intercept: $4$
Answer for screen readers
Slope: $-3$ Y-intercept: $4$
Steps to Solve
- Convert the equation to slope-intercept form
The slope-intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. We need to rearrange the given equation $3x + y = 4$ to isolate $y$ on one side.
- Isolate $y$
Subtract $3x$ from both sides of the equation: $3x + y - 3x = 4 - 3x$
This simplifies to: $y = -3x + 4$
- Identify the slope
Now that the equation is in the form $y = mx + b$, we can directly identify the slope $m$ as the coefficient of $x$. In this case, $m = -3$.
- Identify the y-intercept
The y-intercept $b$ is the constant term in the slope-intercept form. In this case, $b = 4$. This means the line crosses the y-axis at the point (0, 4).
Slope: $-3$ Y-intercept: $4$
More Information
The slope-intercept form is a useful way to represent a linear equation because it allows you to quickly identify the slope and y-intercept, which are essential for graphing the line.
Tips
A common mistake is not correctly rearranging the equation into slope-intercept form before identifying the slope and y-intercept. Make sure to isolate $y$ first. Another mistake can occur when identifying the slope if you dont carry over the negative sign.
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