To find the equation of the linear function in slope-intercept form $y = mx + b$, we need to determine the slope $m$ and the y-intercept $b$.

Step 1: Find the slope ($m$)

The slope $m$ is given by the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Choose any two points from the table. Let's take the points $(1, -5)$ and $(2, -8)$:

$m = \frac{-8 - (-5)}{2 - 1} = \frac{-8 + 5}{1} = \frac{-3}{1} = -3$

So, the slope $m$ is $-3$.

Step 2: Find the y-intercept ($b$)

Now that we know the slope, we can use one of the points from the table to find the y-intercept $b$. Let's use the point $(1, -5)$ and plug it into the equation $y = mx + b$:

$-5 = -3(1) + b$ $-5 = -3 + b$ $b = -5 + 3 = -2$

Final Equation

The equation of the linear function is: $y = -3x - 2$

Would you like further clarification or details on any steps?

Related Questions:

1. How do you find the slope if the points are not integers?
2. Can you determine the equation of a line if only one point and the slope are known?
3. How can you find the slope of a line parallel to a given one?
4. What does the slope of a line represent in real-world applications?
5. How do you find the equation of a line perpendicular to a given one?

Tip:

Always double-check the slope calculation using two points, as small errors in subtraction can lead to an incorrect equation.