Given 2x + 3y = 3, identify the slope and y-intercept.
Understand the Problem
The question is asking to identify the slope (m) and y-intercept (b) of the given linear equation, which is 2x + 3y = 3. This requires rearranging the equation into slope-intercept form (y = mx + b) for analysis.
Answer
m = $-\frac{2}{3}$, b = $1$
Answer for screen readers
m = $-\frac{2}{3}$
b = $1$
Steps to Solve
- Rearranging the Equation We start with the equation given: $$ 2x + 3y = 3 $$
To identify the slope and the y-intercept, we rearrange this into slope-intercept form, which is $y = mx + b$.
- Isolating y Subtract $2x$ from both sides: $$ 3y = 3 - 2x $$
Now, divide everything by 3 to solve for $y$: $$ y = -\frac{2}{3}x + 1 $$
- Identifying the Slope and y-Intercept In the slope-intercept form $y = mx + b$, we can identify:
- The slope $m = -\frac{2}{3}$
- The y-intercept $b = 1$
m = $-\frac{2}{3}$
b = $1$
More Information
The slope of a line indicates its steepness, while the y-intercept is the point where the line crosses the y-axis. In this case, the slope of $-\frac{2}{3}$ indicates that for every 3 units you move to the right, the line drops by 2 units.
Tips
- Forgetting to correctly isolate $y$ can lead to incorrect identification of the slope and intercept.
- Misreading the signs of the slope and intercept can also result in errors.
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