Questions: Find the slope and the y-intercept of the line. -2x-3y=-9 Write your answers in simplest form. slope: y-intercept:

Find the slope and the y-intercept of the line. -2x-3y=-9 Write your answers in simplest form. slope: y-intercept:
Transcript text: Find the slope and the $y$-intercept of the line. \[ -2 x-3 y=-9 \] Write your answers in simplest form. slope: $\square$ $y$-intercept: $\square$
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Solution

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Solution Steps

To find the slope and the y-intercept of the line given by the equation \(-2x - 3y = -9\), we need to convert the equation into the slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

  1. Isolate \(y\) on one side of the equation.
  2. Simplify the equation to identify the slope \(m\) and the y-intercept \(b\).
Step 1: Rearranging the Equation

We start with the equation of the line: \[ -2x - 3y = -9 \] To find the slope and y-intercept, we rearrange this equation into the slope-intercept form \(y = mx + b\).

Step 2: Isolating \(y\)

We isolate \(y\) by adding \(2x\) to both sides and then dividing by \(-3\): \[ -3y = 2x - 9 \] \[ y = -\frac{2}{3}x + 3 \]

Step 3: Identifying the Slope and Y-Intercept

From the equation \(y = -\frac{2}{3}x + 3\), we can identify:

  • The slope \(m = -\frac{2}{3}\)
  • The y-intercept \(b = 3\)

Final Answer

The slope is \(\boxed{-\frac{2}{3}}\) and the y-intercept is \(\boxed{3}\).

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