To find the equation of a line in slope-intercept form ($y = mx + b$), we follow these steps:

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Step 1: Recall the slope-intercept form of the line

The general form is: $y = mx + b$ Where:

• $m$ is the slope of the line.
• $b$ is the y-intercept, which is the value of $y$ when $x = 0$.

Here, the slope $m = -\frac{4}{3}$ is given, and the line passes through the point $(9, -2)$.

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Step 2: Substitute the slope and the point into the line equation

At the point $(9, -2)$, the coordinates $x = 9$ and $y = -2$. Plug these values into the equation $y = mx + b$: $-2 = -\frac{4}{3}(9) + b$

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Step 3: Solve for $b$ (the y-intercept)

Simplify $-\frac{4}{3}(9)$: $-\frac{4}{3}(9) = -12$ Thus: $-2 = -12 + b$ Add $12$ to both sides to solve for $b$: $b = -2 + 12$ $b = 10$

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Step 4: Write the final equation

Now that we know $m = -\frac{4}{3}$ and $b = 10$, substitute these into the slope-intercept form: $y = -\frac{4}{3}x + 10$

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Final Answer:

The equation of the line in slope-intercept form is: $y = -\frac{4}{3}x + 10$

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Would you like me to graph this line or verify it with additional calculations? 😊

5 Related Questions:

1. How do you convert a slope-intercept form equation into standard form?
2. What is the significance of the slope value in the line equation?
3. How do you find the equation of a line if two points are given instead of one?
4. How does the y-intercept change the position of the line on the graph?
5. What happens to the line if the slope is positive instead of negative?

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Tip:

Always double-check calculations when solving for $b$ to avoid arithmetic errors!