Question: Find the rule of the linear function in slope-intercept form using the given points: $(-2, 10)$ and $(5, -4)$
1. **State the problem:** Find the equation of the line in slope-intercept form $y = mx + b$ that passes through the points $(-2, 10)$ and $(5, -4)$.
2. **Formula for slope:** The slope $m$ is given by $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ where $(x_1, y_1) = (-2, 10)$ and $(x_2, y_2) = (5, -4)$.
3. **Calculate the slope:**
$$m = \frac{-4 - 10}{5 - (-2)} = \frac{-14}{7} = \cancel{\frac{-14}{7}} = -2$$
4. **Use slope-intercept form:**
$$y = mx + b$$
Substitute $m = -2$:
$$y = -2x + b$$
5. **Find $b$ using one point:** Use point $(-2, 10)$:
$$10 = -2(-2) + b$$
$$10 = 4 + b$$
$$b = 10 - 4 = 6$$
6. **Final equation:**
$$y = -2x + 6$$
This is the rule of the linear function in slope-intercept form.