Find the equation of the linear function represented by the table below in slope-intercept form.
x	y
1 −5
2 −8
3 −11
4 −14


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.

Find the equation of the linear function represented by the table below in slope-intercept form.
x	y
1	−5
2	−8
3	−11
4	−14

Learn how to find the equation of a linear function in slope-intercept form using a table of values. This problem covers essential algebraic concepts such as slope calculation and y-intercept determination. Suitable for students in Grades 7-8.

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