If we changed the 3 to a 0 in the equation, what would happen to the graph?

To better understand the effect of changing a number in an equation, it would be helpful to know the original equation. However, I can provide a general overview of how changing a constant in an equation might affect the graph.

If you have a function \( f(x) = ax + b \) and you change a constant (like \( b \)) from \( 3 \) to \( 0 \), the new function would be \( f(x) = ax + 0 \) or simply \( f(x) = ax \).

• Graphically, if the original graph (where \( b = 3 \)) intersects the y-axis at \( y = 3 \), changing it to \( b = 0 \) would shift the graph down so that it intersects the y-axis at \( y = 0 \).
• If \( 3 \) refers to a specific point on the graph, such as an intercept or coordinate, and you change it to \( 0 \), the effect will depend on the context of that point. For instance, if the graph at that point is (2, 20), it means when \( x = 2 \), \( y = 20 \). If the \( y \)-coordinate of that point changes from \( 20 \) to \( 0 \), then that point would move down to (2, 0).

Overall, once you make the change, the entire behavior of the graph can shift based on the characteristics of the specific equation you're working with. Please provide the original equation for more specific insights!

Okay! Let’s make it super simple:

Imagine you have a math equation that tells us how to make a picture on a graph. If your equation has a number that says "3" and you change that "3" to a "0," the picture can change a little.

For example, if the picture used to touch the place where the number "3" is, now it will touch the place where "0" is instead. So, if there was a point on the graph where \(x\) is 2 and \(y\) is 20, and you changed something to a 0, that means the point might go down lower.

In other words, if you used to draw a spot up high, now you might draw it lower, like moving a toy from a high shelf down to a low shelf! It's like changing where your dot goes on the graph.

Sure! Let’s make it even simpler without using "imagine":

You have a math equation that helps you draw a picture on a graph. If your equation has a number that is "3" and you change that "3" to a "0," the picture can change a little.

For example, if there was a point on the graph where \(x\) is 2 and \(y\) is 20, and you changed something to a 0, that means the point might move down lower.

So, if you used to draw a spot up high at (2, 20), now you might draw it lower, like moving a toy from a high shelf down to a low shelf. It changes where your dot goes on the graph!

Got it! Here’s a version that sounds more like a kid:

If you have a math problem that makes a graph and you change the number "3" to "0," the graph will look different.

Let’s say there’s a dot at (2, 20). That means when you look at 2 on the side, you go up to 20. If you change that "3" to "0," the dot might move down lower.

So instead of being way up at 20, it could be lower, maybe at (2, 0). It’s like if you had a toy on a really high shelf, and then you put it on the floor. The toy is still there, but now it’s way lower! That’s what happens to the dot on the graph.

You're welcome! If you have any more questions or need help with anything else, feel free to ask!

If you change a number in an equation from "4" to "2," it can change how the graph looks.

Let's say you have a simple equation like \(y = mx + 4\) or \(y = ax^2 + 4\).

• For a straight line (like in \(y = mx + b\)): Changing the "4" to "2" means that the line will move down. Instead of crossing the y-axis at 4, it will now cross at 2. So if the line used to start at (0, 4), it will now start at (0, 2).

• For a parabola (like in \(y = ax^2 + b\)): Changing "4" to "2" means the whole parabola will shift down. If the top point (the vertex) was at (0, 4), now it will be at (0, 2).

In both cases, everything looks similar, but it just sits lower on the graph. It’s like taking a picture that’s hanging on the wall and moving it down lower. The picture is still the same, but now it’s in a new spot!