Question

Type the equation that shows the pattern among this set of ordered pairs.

(0, -5), (1, 0), (2, 5), (3, 10)

Answer 1

First find the slope between any two points:


`\sf Slope=(y_2-y_1)/(x_2-x_1)`

Where
`\sf (x_1,y_1),(x_2,y_2)` are the two points

So calculating the slope:


`\sf Slope=(5-0)/(2-1)=(5)/(1)=5`

So the slope is
`\boxed{5}`

And our equation will be in the format of
`\sf y=mx+b`
where
`\sf m~ is~ the ~slope` and
`\sf b ~is~the~y-intercept`

So, now we have half of the equation:


`\sf y= 5x+b`

Now to calculate b, we can plug in a point
`\sf (x,y)` and solve for b.

So


`\sf y= 5x+b`

Lets use the point

`\sf (1,0) which ~is~in~the~form ~of ~(x,y)`

So:

`\sf 0=5(1)+b`

And then:

`\sf b=-5`

So our final equation is
`\sf \boxed{y=5x-5}`