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=(y_2-y_1)/(x_2-x_1)=(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.