https://file.aiquickdraw.com/mathbot/file/172614848423956yyhni1.jpg

The equation given is \( y = -4x - 5 \). We need to find the \( y \)-coordinate for each value of \( x \), and answer the following questions.

### Step 1: Finding the \( y \)-coordinates
We will substitute the values of \( x \) (0, 1, 2, 3) into the equation to calculate the corresponding \( y \)-values.

- For \( x = 0 \):
  \[
  y = -4(0) - 5 = -5
  \]
  So, \( y = -5 \).

- For \( x = 1 \):
  \[
  y = -4(1) - 5 = -4 - 5 = -9
  \]
  So, \( y = -9 \).

- For \( x = 2 \):
  \[
  y = -4(2) - 5 = -8 - 5 = -13
  \]
  So, \( y = -13 \).

- For \( x = 3 \):
  \[
  y = -4(3) - 5 = -12 - 5 = -17
  \]
  So, \( y = -17 \).

### Step 2: Filling the Table
The table with \( x \)- and \( y \)-coordinates is:
\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
0 & -5 \\
1 & -9 \\
2 & -13 \\
3 & -17 \\
\hline
\end{array}
\]

### Step 3: Initial Function Value
The initial value of the function occurs when \( x = 0 \). From the calculations above, when \( x = 0 \), \( y = -5 \). So, the function's initial value is \( -5 \).

### Step 4: Change in \( y \)-value per Unit Increase in \( x \)
The change in \( y \)-value for each 1-unit increase in \( x \) is the slope of the equation, which is \( -4 \). This means that for every increase of 1 in \( x \), the \( y \)-value decreases by 4.

---

Would you like further details or have any questions?

### Related Questions:
1. How do you determine the slope from a linear equation?
2. What is the relationship between the slope and the change in \( y \)-value?
3. How would the equation change if the slope were positive?
4. What does the \( y \)-intercept represent in a linear equation?
5. How can you graph a linear equation based on this table?

### Tip:
When solving linear equations, always look at the slope and \( y \)-intercept to quickly understand how the graph behaves and how the values change.

For the equation y = -4x - 5, find the y-coordinate for each value of x (0, 1, 2, 3). Also, find the initial value when x = 0 and determine how much the y-value changes for each 1-unit increase in the x-value.

Learn how to solve the linear equation y = -4x - 5 by finding y-coordinates for values of x (0, 1, 2, 3). This solution covers important concepts like slope, y-intercept, and changes in y-value for each unit increase in x. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation