Match each statement with its corresponding graph in choices A...

Question

Match each statement with its corresponding graph in choices A–D. In each case, k > 0. y varies directly as x. (y=kx)

Four graphs labeled A to D showing different curves and a line on xy-axes, illustrating various relationships between x and y.

Accepted Answer

Welcome back. I am so glad you're here. We are told to draw the graph for the following variation problem to use the symbol K for the constant of variation. Our variation problem is Y varies directly as X. All right, let's start by looking at our variation problem and turn that into an equation. When we are given Y that's Y equals, we can start with that. And we're told it varies directly. We recall from previous lessons that variation direct variation means to multiply we multiply our constant by whatever's left. And so we have the constant term, which in this case is K multiplied by what's left and what's left is just X. So it's Y equals K multiplied by X. Now, what kind of equation is this? Well, this is the equation of a line. We recall from previous lessons. The equation of a line Y equals M X plus B where M is the slope. In this case, our slope is K and B is the Y intercept. In this case, there's no given Y intercept. So it's zero, which means that this passes through the origin. And what do we know about our slope K. Well, we know that K is greater than zero. So it's a positive slope. We don't know how big it is. It could be a very big number for our slope. It could be a very small fraction for our slope, but it's going to be positive in any case. So now we have enough information to graph this, we can draw a vertical y axis, a horizontal X axis. They come together the origin in the middle. We know that our line is going to pass through the origin and that it's going to be a positive slope. So from the origin as it heads toward positive X values, it will also head toward positive Y values. And likewise, with a positive slope, when we have negative X values, we also have negative Y values. So we can draw our line passing through the origin. A straight line heading toward positive infinity for both X and Y and simultaneously heading toward negative infinity for X and Y. All right, there's our graph well done. We'll catch you on the next one.

Match each statement with its corresponding graph in choices A–D. In each case, k > 0. y varies directly as x. (y=kx)

Key Concepts

Direct Variation

Slope of a Linear Function

Graphing Linear Equations

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