What is the slope and y-intercept for the equation y = 2/3x + 5?
Understand the Problem
The question is asking to identify the slope and y-intercept from the given linear equation y = (2/3)x + 5. We need to analyze the equation to determine the correct slope and y-intercept values.
Answer
The slope is $\frac{2}{3}$ and the y-intercept is 5.
Answer for screen readers
The slope is $\frac{2}{3}$ and the y-intercept is 5.
Steps to Solve
- Identify the slope from the equation
The given equation is in the slope-intercept form, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. In this case, we can see that:
$$ m = \frac{2}{3} $$
Thus, the slope is $\frac{2}{3}$.
- Identify the y-intercept from the equation
Similarly, the y-intercept $b$ can be found directly from the equation. Here, we see that:
$$ b = 5 $$
So, the y-intercept is 5.
- Summarize the findings
Now, we can summarize that the slope is $\frac{2}{3}$ and the y-intercept is 5.
The slope is $\frac{2}{3}$ and the y-intercept is 5.
More Information
In linear equations, the slope indicates the steepness and direction of the line, while the y-intercept indicates where the line crosses the y-axis. This particular equation represents a line that rises gently due to the fractional slope.
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