To find the equation of the linear function $y = mx + b$ that passes through the points $(-2, 5)$ and $(1, -4)$, we need to follow these steps:

Step 1: Find the slope $m$

The slope $m$ is given by the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Here, $(x_1, y_1) = (-2, 5)$ and $(x_2, y_2) = (1, -4)$.

Substituting the values: $m = \frac{-4 - 5}{1 - (-2)} = \frac{-4 - 5}{1 + 2} = \frac{-9}{3} = -3$

Step 2: Find the y-intercept $b$

Now that we have the slope $m = -3$, we can use one of the points to solve for $b$. Let’s use the point $(-2, 5)$ and substitute it into the equation $y = mx + b$.

Substituting $y = 5$, $m = -3$, and $x = -2$: $5 = -3(-2) + b$ $5 = 6 + b$ $b = 5 - 6 = -1$

Step 3: Write the equation

Now that we have the slope $m = -3$ and the y-intercept $b = -1$, the equation of the line is: $y = -3x - 1$

Final Answer:

The equation of the line passing through the points $(-2, 5)$ and $(1, -4)$ is: $y = -3x - 1$

Would you like more details or have any questions?

Here are 5 related questions:

1. How do you find the slope of a line given two points?
2. What does the slope represent in a linear function?
3. How would the equation change if the points were reversed?
4. Can you find the x-intercept for the equation $y = -3x - 1$?
5. What is the general form of a linear equation, and how does it relate to the slope-intercept form?

Tip: When finding the slope, make sure to subtract the coordinates in the same order to avoid mistakes!