Question

1. In the Gizmo, plot the points (1, 3) and (4, 6).A. What is the equation of this line?y = x+2 B. Drag the probe so that it passes through the point (1, 3). Substitute the input (x) andOutput (y) values into the equation. Describe the result.

Answer 1

Part a

For this case we have two points given (1,3) and (4,6) and we want to find the equation for this line and we can use this equation:

$y=mx+b$

Where m represent the slope and b the intercept. We can estimate the slope with this formula:

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{6-3}{4-1}=1$

And then we can find the intercept from one point given and replacing into the equation like this:

$3=1\cdot1+b\rightarrow b=2$

And the equation would be:

$y=x+2$

Part b

Now we just need to see if the point (1,3) is on the line calculated let's check this. If x=1 we have that:

$y=1\cdot1+2=3$

So then we verify that the point is on the line and then that would be the proof for this case.