a line has a slope of $-\frac{2}{3}$ and passes through the point $(9, 0)$. write its equation in slope…

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. We know that $m=-\frac{2}{3}$ and the line passes through the point $(x,y)=(9,0)$.

Step2: Substitute values into the equation

Substitute $m = -\frac{2}{3}$, $x = 9$ and $y = 0$ into $y=mx + b$: [ \begin{align*} 0&=-\frac{2}{3}(9)+b\ 0&=-6 + b \end{align*} ]

Step3: Solve for $b$

To solve for $b$, add 6 to both sides of the equation $0=-6 + b$: [ \begin{align*} 0+6&=-6 + b+6\ b&=6 \end{align*} ]

Step4: Write the equation

Now that we know $m = -\frac{2}{3}$ and $b = 6$, substitute these values into the slope - intercept form $y=mx + b$: $y=-\frac{2}{3}x+6$

Answer:

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