Questions: Write the equation 2x+3y=9 in slope-intercept form.

Transcript text: 4. Write the equation $2 x+3 y=9$ in slope-intercept form.

Solution

Solution Steps

To convert the given equation $2x + 3y = 9$ into slope-intercept form $y = mx + b$, we need to solve for $y$ in terms of $x$. This involves isolating $y$ on one side of the equation.

Step 1: Start with the Given Equation

We start with the given equation: \[ 2x + 3y = 9 \]

Step 2: Isolate the $ y $-term

Subtract $ 2x $ from both sides to isolate the $ y $-term: \[ 3y = 9 - 2x \]

Step 3: Solve for $ y $

Divide both sides by 3 to solve for $ y $: \[ y = \frac{9 - 2x}{3} \]

Step 4: Simplify the Expression

Simplify the right-hand side: \[ y = 3 - \frac{2x}{3} \]

Final Answer

The equation in slope-intercept form is: \[ \boxed{y = -\frac{2}{3}x + 3} \]

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