Questions: a. Rewrite the given equation in slope-intercept form. b. Give the slope and y-intercept. c. Use the slope and y-intercept to graph the linear function. 61. 2x + 3y - 18 = 0

a. Rewrite the given equation in slope-intercept form.
b. Give the slope and y-intercept.
c. Use the slope and y-intercept to graph the linear function.
61. 2x + 3y - 18 = 0

Transcript text: a. Rewrite the given equation in slope-intercept form. b. Give the slope and y-intercept. c. Use the slope and $y$-intercept to graph the linear function. 61. $2 x+3 y-18=0$

Solution

Solution Steps

Step 1: Rewrite the equation in slope-intercept form

The given equation is $2x + 3y - 18 = 0$. To rewrite it in slope-intercept form $y = mx + b$, solve for $y$:

\[ 3y = -2x + 18 \]

\[ y = -\frac{2}{3}x + 6 \]

Step 2: Identify the slope and y-intercept

From the equation $y = -\frac{2}{3}x + 6$, the slope $m$ is $-\frac{2}{3}$ and the y-intercept $b$ is $6$.

Step 3: Use the slope and y-intercept to graph the linear function

The linear function can be graphed using the slope $-\frac{2}{3}$ and y-intercept $6$.

Final Answer

Slope: $-\frac{2}{3}$
Y-intercept: $6$

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