To find the slope-intercept form $y = mx + b$ of the line passing through the points $(-3, 1)$ and $(0, -5)$, follow these steps:

Step 1: Find the slope $m$

The formula for slope is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting the given points $(-3, 1)$ and $(0, -5)$: $m = \frac{-5 - 1}{0 - (-3)} = \frac{-6}{3} = -2$

Step 2: Use the slope-intercept form $y = mx + b$

We know the slope $m = -2$. To find $b$ (the y-intercept), substitute one point into the equation. Using $(0, -5)$, where $x = 0$ and $y = -5$: $-5 = -2(0) + b$ $b = -5$

Step 3: Write the equation

Substitute $m = -2$ and $b = -5$ into $y = mx + b$: $y = -2x - 5$

Final Answer:

The slope-intercept form of the line is: $y = -2x - 5$

Would you like to see a graph or further details about how to check this result?

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1. How do we find the slope if given different points?
2. What is the meaning of $b$ (the y-intercept)?
3. How does changing the slope affect the graph?
4. Can we rewrite this equation in standard form?
5. How can we verify the line passes through both points?

Tip: Always double-check your slope calculation to avoid sign errors!