Question

Graph the two equations: "y" equals negative 3 "x" plus 4y=−3x+4 and "y" equals 3 "x" minus 2y=3x−2 Step 1️⃣: Graph the equations by typing them below. Step 2️⃣: Place the red dot where the two lines intersect.

Answer 1

To graph the two equations, let's first rewrite them in slope-intercept form \(y = mx + b\).

1. **Equation 1:** \(y = -3x + 4\)
- This line has a slope of \(-3\) and a y-intercept at \(4\).

2. **Equation 2:** \(y = 3x - 2\)
- This line has a slope of \(3\) and a y-intercept at \(-2\).

### Step 1: Graph the equations

You can visualize the graphs of the equations as follows:

1. **For \(y = -3x + 4\)**:
- Start at the point \((0, 4)\) (y-intercept).
- From there, move down \(3\) units and right \(1\) unit to plot the second point \((1, 1)\).
- Draw the line through these points.

2. **For \(y = 3x - 2\)**:
- Start at the point \((0, -2)\) (y-intercept).
- From there, move up \(3\) units and right \(1\) unit to plot the second point \((1, 1)\).
- Draw the line through these points.

### Step 2: Find the intersection point

Now, let's solve for the intersection of these lines by setting the two equations equal to each other:

\[
-3x + 4 = 3x - 2
\]

Combine like terms:

\[
4 + 2 = 3x + 3x
\]
\[
6 = 6x
\]

Divide both sides by \(6\):

\[
x = 1
\]

Now, substitute \(x = 1\) into either of the original equations to find \(y\):

Using \(y = -3x + 4\):
\[
y = -3(1) + 4 = -3 + 4 = 1
\]

So, the intersection point is \((1, 1)\).

### Conclusion

The two equations graph as follows:
- **Line 1:** \(y = -3x + 4\)
- **Line 2:** \(y = 3x - 2\)

And they intersect at the point marked with a red dot at \((1, 1)\).

If you're graphing these by hand or using graphing software, you can plot the lines and mark the intersection point accordingly.