Questions: -2x - 3y = 3 Slope and y intercept

-2x - 3y = 3 Slope and y intercept
Transcript text: -2 x-3 y=3 Slope and $y$ intercept
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Solution

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Solution Steps

To find the slope and y-intercept of the given linear equation, we need to rewrite it in the slope-intercept form, \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. We will solve for \( y \) in terms of \( x \).

Step 1: Rewrite the Equation

The given equation is \( -2x - 3y = 3 \). We will rearrange this equation to isolate \( y \) and express it in the slope-intercept form \( y = mx + b \).

Step 2: Solve for \( y \)

Rearranging the equation gives us: \[ -3y = 2x + 3 \] Dividing both sides by \(-3\) results in: \[ y = -\frac{2}{3}x - 1 \]

Step 3: Identify the Slope and Y-Intercept

From the equation \( y = -\frac{2}{3}x - 1 \), we can identify the slope \( m \) and the y-intercept \( b \):

  • Slope \( m = -\frac{2}{3} \)
  • Y-Intercept \( b = -1 \)

Final Answer

The slope is \( m = -\frac{2}{3} \) and the y-intercept is \( b = -1 \). Thus, the final answers are: \[ \boxed{m = -\frac{2}{3}} \] \[ \boxed{b = -1} \]

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