Question

Graph the following y=4x+3 and y=-x-2
What are the cordinates

Answer 1

To graph the equations \( y = 4x + 3 \) and \( y = -x - 2 \), we can first find their points of intersection.

1. **Finding the Intersection**:
Set the two equations equal to each other:
\[
4x + 3 = -x - 2
\]

Now, solve for \( x \):
\[
4x + x = -2 - 3 \\
5x = -5 \\
x = -1
\]

Now substitute \( x = -1 \) back into either equation to find \( y \). Using \( y = 4x + 3 \):
\[
y = 4(-1) + 3 \\
y = -4 + 3 \\
y = -1
\]

So, the coordinates of the intersection point are:
\[
(-1, -1)
\]

2. **Finding Additional Points**:
You can also find points on each line to help with graphing.

For \( y = 4x + 3 \):
- Let \( x = 0 \):
\[
y = 4(0) + 3 = 3 \quad \Rightarrow \quad (0, 3)
\]
- Let \( x = 1 \):
\[
y = 4(1) + 3 = 7 \quad \Rightarrow \quad (1, 7)
\]

For \( y = -x - 2 \):
- Let \( x = 0 \):
\[
y = -0 - 2 = -2 \quad \Rightarrow \quad (0, -2)
\]
- Let \( x = 1 \):
\[
y = -1 - 2 = -3 \quad \Rightarrow \quad (1, -3)
\]

3. **Prepare to Graph**:
Now you have points from both lines:
- Line 1 (\( y = 4x + 3 \)): \( (0, 3), (1, 7), (-1, -1) \)
- Line 2 (\( y = -x - 2 \)): \( (0, -2), (1, -3), (-1, -1) \)

4. **Graphing**:
Plot the points on a coordinate plane:
- \( (0, 3) \) and \( (1, 7) \) for \( y = 4x + 3 \), and draw the line through these points.
- \( (0, -2) \) and \( (1, -3) \) for \( y = -x - 2 \), and draw the line through these points.

5. **Conclusion**:
The coordinates of the intersection point are \( (-1, -1) \). You can also graph both equations and observe their slopes and intercepts to fully understand their relationship.