Question

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

Answer 1

First find the slope between any two points:

$\sf Slope=\frac{y_2-y_1}{x_2-x_1}$

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

So calculating the slope:

$\sf Slope=\frac{5-0}{2-1}=\frac{5}{1}=5$

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 $\sf \boxed{y=5x-5}$