The problem requires us to find two points for each of the given linear equations, $y = 3x - 5$ and $y = -4x + 9$, so we can draw these lines on the graph.

1. Problem Description

The problem requires us to find two points for each of the given linear equations, $y = 3x - 5$ and $y = -4x + 9$, so we can draw these lines on the graph.

2. Solution Steps

Let's find two points for the first equation, $y = 3x - 5$:

Step 1: Choose a value for $x$, say $x = 0$.

Step 2: Substitute $x = 0$ into the equation:

$y = 3(0) - 5 = -5$

So, one point is $(0, -5)$.

Step 3: Choose another value for $x$, say $x = 1$.

Step 4: Substitute $x = 1$ into the equation:

$y = 3(1) - 5 = 3 - 5 = -2$

So, another point is $(1, -2)$.

Thus, the two points for $y = 3x - 5$ are $(0, -5)$ and $(1, -2)$.

Now, let's find two points for the second equation, $y = -4x + 9$:

Step 1: Choose a value for $x$, say $x = 0$.

Step 2: Substitute $x = 0$ into the equation:

$y = -4(0) + 9 = 9$

So, one point is $(0, 9)$.

Step 3: Choose another value for $x$, say $x = 1$.

Step 4: Substitute $x = 1$ into the equation:

$y = -4(1) + 9 = -4 + 9 = 5$

So, another point is $(1, 5)$.

Thus, the two points for $y = -4x + 9$ are $(0, 9)$ and $(1, 5)$.

3. Final Answer

For $y = 3x - 5$, two points are $(0, -5)$ and $(1, -2)$.

For $y = -4x + 9$, two points are $(0, 9)$ and $(1, 5)$.