Question

What is the slope-intercept form of the function described by this table?



x 1 2 3 4
y 1 −2 −5 −8
Enter your answer by filling in the boxes.

y =
x +

Answer 1

To find the slope-intercept form of the function described by the given table, we first need to determine the slope (m) and the y-intercept (b).

The given points are:
- (1, 1)
- (2, -2)
- (3, -5)
- (4, -8)

**Step 1: Calculate the slope (m)**

The slope \( m \) can be calculated using any two points from the table. We'll use the points (1, 1) and (2, -2).

The formula for the slope between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting our points:
\[
m = \frac{-2 - 1}{2 - 1} = \frac{-3}{1} = -3
\]

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

We can use the slope-intercept form of a line, which is:
\[
y = mx + b
\]
We can plug in one of the points to find \( b \). Let's use the point (1, 1):
\[
1 = -3(1) + b
\]
\[
1 = -3 + b
\]
Adding 3 to both sides gives:
\[
b = 4
\]

**Final Equation**

Now we can write the equation in slope-intercept form:
\[
y = -3x + 4
\]

Thus, filling in the blanks:
- y = -3
- x + 4

So, the final answer is:
\[
y = -3x + 4
\]