Question

Graph these equations:
y = -x +1
y = -6/5x

Answer 1

To graph the equations \( y = -x + 1 \) and \( y = -\frac{6}{5}x \), we need to determine a few key points for each equation.

### 1. Graphing \( y = -x + 1 \)

This is a linear equation in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

- **Y-intercept**: Set \( x = 0 \):
\[
y = -0 + 1 = 1
\]
So the point is \( (0, 1) \).

- **X-intercept**: Set \( y = 0 \):
\[
0 = -x + 1 \implies x = 1
\]
So the point is \( (1, 0) \).

- **Slope**: The slope \( m = -1 \), which indicates a line descending from left to right.

**Points to plot**:
- \( (0, 1) \)
- \( (1, 0) \)

### 2. Graphing \( y = -\frac{6}{5}x \)

This is also in slope-intercept form.

- **Y-intercept**: Set \( x = 0 \):
\[
y = -\frac{6}{5} \cdot 0 = 0
\]
So the point is \( (0, 0) \).

- **X-intercept**: Set \( y = 0 \):
\[
0 = -\frac{6}{5}x \implies x = 0
\]
So the point is \( (0, 0) \).

- **Slope**: The slope is \( -\frac{6}{5} \), which indicates a steep line descending from left to right.

**Points to plot**:
- \( (0, 0) \)
- To find another point, you can choose \( x = 5 \):
\[
y = -\frac{6}{5}(5) = -6
\]
So another point is \( (5, -6) \).

### Summary of Points to Plot:
- For \( y = -x + 1 \):
- \( (0, 1) \)
- \( (1, 0) \)

- For \( y = -\frac{6}{5}x \):
- \( (0, 0) \)
- \( (5, -6) \)

### Steps to Graph:

1. Plot the points for each line on the coordinate axes.
2. For \( y = -x + 1 \), draw a straight line through \( (0, 1) \) and \( (1, 0) \).
3. For \( y = -\frac{6}{5}x \), draw a straight line through \( (0, 0) \) and \( (5, -6) \).

### Visual Representation:
If you need to visualize this, you can plot these points on graph paper or use a graphing tool. The intersection point of the two lines will give you the solution to the system of equations.