graph -5x+y=1 subbing in arbituary values

To graph the equation \(-5x + y = 1\) by substituting arbitrary values for \(x\) and finding the corresponding values of \(y\), follow these steps:

### 1. Rearrange the Equation (if needed)
First, solve for \(y\) in terms of \(x\):
\[
y = 5x + 1
\]
This equation is now in the form \(y = mx + c\), where \(m = 5\) is the slope and \(c = 1\) is the y-intercept.

### 2. Choose Arbitrary Values for \(x\)
Let's choose three arbitrary values for \(x\) to substitute into the equation:

- \(x = -1\)
- \(x = 0\)
- \(x = 1\)

### 3. Calculate Corresponding Values of \(y\)
Substitute each value of \(x\) into the equation \(y = 5x + 1\) to find the corresponding \(y\) values:

1. **For \(x = -1\)**:
   \[
   y = 5(-1) + 1 = -5 + 1 = -4
   \]
   Point: \((-1, -4)\)

2. **For \(x = 0\)**:
   \[
   y = 5(0) + 1 = 0 + 1 = 1
   \]
   Point: \((0, 1)\)

3. **For \(x = 1\)**:
   \[
   y = 5(1) + 1 = 5 + 1 = 6
   \]
   Point: \((1, 6)\)

### 4. Plot the Points and Draw the Line
Now, plot the points \((-1, -4)\), \((0, 1)\), and \((1, 6)\) on a coordinate plane. Draw a straight line through these points, extending it in both directions. This line represents the graph of the equation \(-5x + y = 1\).

Would you like me to plot this graph for you?

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**Relative Questions:**

1. What does the slope of the line represent in this equation?
2. How would the graph change if the equation were \(-5x + y = 2\)?
3. What is the significance of the y-intercept in this equation?
4. How can you determine the x-intercept of the graph?
5. How would the graph look if the slope were negative, such as \(y = -5x + 1\)?

**Tip:** When choosing points to plot a line, picking values of \(x\) that are evenly spaced and close to zero can make the graphing process easier.

Learn how to graph the equation -5x + y = 1 by substituting arbitrary values for x and finding corresponding y values. This step-by-step guide includes choosing values, calculating points, and plotting the graph. Suitable for students in Grades 7-9 studying linear equations and graphing.

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